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, Chapter: 1 -Problem: 21 >> A study that surveyed a random sample of otherwise healthy high school students found that they are more likely to get muscle cramps when they are stressed. The study also noted that students drink more coffee and sleep less when they are stressed.(a) What type of study is this?(b) Can this study be used to conclude a causal relationship between increased stress and muscle cramps?(c) State possibl
Answer Preview: (a) This study is an observational study. (b) No, this study cannot be used to conclude a causal rel…

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, Chapter: 1 -Problem: 44 >> The following summary table shows the number of space launches in the US by the type of launching agency and the outcome of the launch (success or failure).(a) What variables were collected on each launch in order to create to the summary table above?(b) State whether each variable is numerical or categorical. If numerical, state whether it is continuous or discrete. If categorical, state whether
Answer Preview: (a) The variables collected on each launch to create the summary table are: Type of Launching Agency…

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, Chapter: 1 -Problem: 16 >> The General Social Survey asked the question, "After an average work day, about how many hours do you have to relax or pursue activities that you enjoy?" to a random sample of 1,155 Americans. The average relaxing time was found to be 1.65 hours. Determine which of the following is an observation, a variable, a sample statistic (value calculated based on the observed sample), or a population param
Answer Preview: (a) An American in the sample: This is an observation. It refers to an individual American wh…

, Chapter: 4 -Problem: 41 >> The American Community Survey estimates that 47.1% of women ages 15 years and over are married.(a) We randomly select three women between these ages. What is the probability that the third woman selected is the only one who is married?(b) What is the probability that all three randomly selected women are married?(c) On average, how many women would you expect to sample before selecting a married w
Answer Preview: To solve these problems, we will use probability calculations based on the given information. Let's start with part (a): (a) Probability that the thir…

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, Chapter: 5 -Problem: 2 >> For each of the following situations, state whether the parameter of interest is a mean or a proportion.(a) A poll shows that 64% of Americans personally worry a great deal about federal spending and the budget deficit.(b) A survey reports that local TV news has shown a 17% increase in revenue within a two year period while newspaper revenues decreased by 6.4% during this time period.(c) In a surv
Answer Preview: (a) The parameter of interest is a proportion. The parameter is the percentage of Ameri…

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, Chapter: 9 -Problem: 20 >> Determine which of the following statements are true and false. For each statement that is false, explain why it is false.(a) Suppose we consider the first two observations based on a logistic regression model, where the first variable in observation 1 takes a value of x1 = 6 and observation 2 has x1 = 4. Suppose we realized we made an error for these two observations, and the first observation wa
Answer Preview: (a) False. The predicted probability from a logistic regression model depends on the values of the predictor variables. If we correct the values of x1 …

, Chapter: 4 -Problem: 47 >> Heights of 10 year olds, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6 inches.(a) What fraction of 10 year olds are taller than 76 inches?(b) If there are 2,000 10 year olds entering Six Flags Magic Mountain in a single day, then compute the expected number of 10 year olds who are at least 76 inches tall. (You may assume the heights of the
Answer Preview: (a) To find the fraction of 10-year-olds taller than 76 inches, we need to calculate the z-score and then find the corresponding area under the normal …

, Chapter: 7 -Problem: 15 >> Air quality measurements were collected in a random sample of 25 country capitals in 2013, and then again in the same cities in 2014. We would like to use these data to compare average air quality between the two years. Should we use a paired or non-paired test? Explain your reasoning.
Answer Preview: To compare the average air quality between the two years (2013 and 2014) for the same set of country …

, Chapter: 7 -Problem: 48 >> The researchers from Exercise 7.47 also investigated the effects of being distracted by a game on how much people eat. The 22 patients in the treatment group who ate their lunch while playing solitaire were asked to do a serial-order recall of the food lunch items they ate. The average number of items recalled by the patients in this group was 4. 9, with a standard deviation of 1.8. The average nu
Answer Preview: To determine if there is strong evidence that the average number of food items recalled by the patients in the treatment and control groups are differ…

, Chapter: 7 -Problem: 18 >> In each of the following scenarios, determine if the data are paired. (a) We would like to know if Intel's stock and Southwest Airlines' stock have similar rates of return. To find out, we take a random sample of 50 days, and record Intel's and Southwest's stock on those same days. (b) We randomly sample 50 items from Target stores and note the price for each. Then we visit Walmart and collect the
Answer Preview: To determine if the data are paired in each scenario, we need to check if there is a one-to-one corr…

, Chapter: 7 -Problem: 53 >> At a startup company running a new weather app, an engineering team generally runs experiments where a random sample of 1% of the app's visitors in the control group and another 1% were in the treatment group to test each new feature. The team's core goal is to increase a metric called daily visitors, which is essentially the number of visitors to the app each day. They track this metric in each e
Answer Preview: (a) To calculate the required standard error, we can use the formula for the standard error of the mean: Standard Error (SE) = (Standard Deviation of the Population) / (Sample Size) We want to detect …

, Chapter: 7 -Problem: 47 >> A group of researchers are interested in the possible effects of distracting stimuli during eating, such as an increase or decrease in the amount of food consumption. To test this hypothesis, they monitored food intake for a group of 44 patients who were randomized into two equal groups. The treatment group ate lunch while playing solitaire, and the control group ate lunch without any added distra
Answer Preview: To determine if there is convincing evidence that the average food intake (measured in the amount of biscuits consumed) is different for the patients …

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, Chapter: 8 -Problem: 19 >> Suppose we fit a regression line to predict the shelf life of an apple based on its weight. For a particular apple, we predict the shelf life to be 4.6 days. The apple's residual is -0.6 days. Did we over or underestimate the shelf-life of the apple? Explain your reasoning.
Answer Preview: We underestimated the shelf-life of the apple. In regression analy…

, Chapter: 7 -Problem: 46 >> Determine if the following statements are true or false, and explain your reasoning for statements you identify as false. If the null hypothesis that the means of four groups are all the same is rejected using ANOVA at a 5% significance level, then ...(a) We can then conclude that all the means are different from one another.(b) The standardized variability between groups is higher than the standa
Answer Preview: (a) False: If the null hypothesis that the means of four groups are all the same is rejected using A…

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, Chapter: 4 -Problem: 43 >> Suppose weights of the checked baggage of airline passengers follow a nearly normal distribution with mean 45 pounds and standard deviation 3.2 pounds. Most airlines charge a fee for baggage that weigh in excess of 50 pounds. Determine what percent of airline passengers incur this fee.
Answer Preview: To determine what percent of airline passengers incur the fee for baggage that weighs in excess of 5…

, Chapter: 7 -Problem: 16 >> Determine if the following statements are true or false. If false, explain. (a) In a paired analysis we first take the difference of each pair of observations, and then we do inference on these differences. (b) Two data sets of different sizes cannot be analyzed as paired data. (c) Consider two sets of data that are paired with each other. Each observation in one data set has a natural corresponde
Answer Preview: (a) True. In a paired analysis, we have two sets of paired observations, and the first step is to ca…

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, Chapter: 8 -Problem: 22 >> The scatterplot below shows the relationship between the number of calories and amount of carbohydrates (in grams) Starbucks food menu items contain. Since Starbucks only lists the number of calories on the display items, we are interested in predicting the amount of carbs a menu item has based on its calorie content.(a) Describe the relationship between number of calories and amount of carbohydra
Answer Preview: (a) In the scatterplot, the relationship between the number of calories and the amount of carbohydrates appears to have a pattern of positive correlat…

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, Chapter: 8 -Problem: 16 >> What would be the correlation between the annual salaries of males and females at a company if for a certain type of position men always made(a) $5,000 more than women?(b) 25% more than women?(c) 15% less than women?
Answer Preview: (a) If for a certain type of position men always made $5,000 more than women, then the correlation b…

, Chapter: 9 -Problem: 11 >> Suppose a social scientist is interested in studying what makes audiences love or hate a movie. She collects a random sample of movies (genre, length, cast, director, budget, etc.) as well as a measure of the success of the movie (score on a film review aggregator website). If as part of her research she is interested in finding out which variables are significant predictors of movie success, what
Answer Preview: For the social scientist's research question of identifying significant predictors of movie success, she should use a statistical method known as "mul…

, Chapter: 8 -Problem: 37 >> Determine if the following statements are true or false. If false, explain why.(a) A correlation coefficient of -0.90 indicates a stronger linear relationship than a correlation of 0.5.(b) Correlation is a measure of the association between any two variables.
Answer Preview: (a) A correlation coefficient of -0 90 indicates a stronger linear relationship than a correlation o…

, Chapter: 8 -Problem: 30 >> Exercise 8.12 introduces data on the average monthly temperature during the month babies first try to crawl (about 6 months after birth) and the average first crawling age for babies born in a given month. A scatterplot of these two variables reveals a potential outlying month when the average temperature is about 53°F and average crawling age is about 28.5 weeks. Does this point have high leverag
Answer Preview: To determine whether the point with an average temperature of about 53F and an average crawling age of about 28 5 weeks is a high leverage or influent…

, Chapter: 6 -Problem: 4 >> About 25% of young Americans have delayed starting a family due to the continued economic slump. Determine if the following statements are true or false, and explain your reasoning. (a) The distribution of sample proportions of young Americans who have delayed starting a family due to the continued economic slump in random samples of size 12 is right skewed. (b) In order for the distribution of sa
Answer Preview: (a) False. The distribution of sample proportions of young Americans who have delayed starting a family due to the continued economic slump in random …

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, Chapter: 7 -Problem: 28 >> Each year the US Environmental Protection Agency (EPA) releases fuel economy data on cars manufactured in that year. Below are summary statistics on fuel efficiency (in miles/gallon) from random samples of cars with manual and automatic transmissions. Do these data provide strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms o
Answer Preview: Let: Group 1: Automatic Group 2: Manual H 0 : 1 - 2 = 0 Ha : 1 - 2 0 T…

, Chapter: 6 -Problem: 6 >> The Marist Poll published a report stating that 66% of adults nationally think licensed drivers should be required to retake their road test once they reach 65 years of age. It was also reported that interviews were conducted on 1,018 American adults, and that the margin of error was 3% using a 95% confidence level.(a) Verify the margin of error reported by The Marist Poll. (b) Based on a 95% conf
Answer Preview: To verify the margin of error reported by The Marist Poll, we can calculate it using the given sample size and confidence level. (a) Margin of Error C…

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, Chapter: 7 -Problem: 11 >> Georgianna claims that in a small city renowned for its music school, the average child takes less than 5 years of piano lessons. We have a random sample of 20 children from the city, with a mean of 4.6 years of piano lessons and a standard deviation of 2.2 years. (a) Evaluate Georgianna's claim (or that the opposite might be true) using a hypothesis test. (b) Construct a 95% confidence interval f
Answer Preview: To evaluate Georgianna's claim about the average number of years children in the city take piano lessons, we can perform a hypothesis test and constru…

, Chapter: 6 -Problem: 19 >> A study asked 1,924 male and 3,666 female undergraduate college students their favorite color. A 95% confidence interval for the difference between the proportions of males and females whose favorite color is black (pmale - Pfemale) was calculated to be (0.02, 0.06). Based on this information, determine if the following statements about undergraduate college students are true or false, and explain
Answer Preview: Let's go through each statement one by one: (a) We are 95% confident that the true proportion of males whose favorite color is black is 2% lower to 6% …

, Chapter: 5 -Problem: 26 >> In each part below, there is a value of interest and two scenarios (I and II). For each part, report if the value of interest is larger under scenario I, scenario II, or whether the value is equal under the scenarios.(a) The standard error of p? when (I) n = 125 or (II) n = 500.(b) The margin of error of a confidence interval when the  confidence level is (I) 90% or (II) 80%.(c) The p-value for a
Answer Preview: To compare the values of interest under different scenarios, we need more information or assumptions about the specific situations. However, I can pro…

, Chapter: 6 -Problem: 14 >> Exercise 6.12 presents the results of a poll where 48% of 331 Americans who decide to not go to college do so because they cannot afford it. (a) Calculate a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it, and interpret the interval in context. (b) Suppose we wanted the margin of error for the 90% confidence level to be about 1.
Answer Preview: (a) To calculate a 90% confidence interval for the proportion of Americans who decide not to go to c…

, Chapter: 4 -Problem: 9 >> Exercise 4.7 states that average daily high temperature in June in LA is 77°F with a standard deviation of 5°F, and it can be assumed that they to follow a normal distribution. We use the following equation to convert °F (Fahrenheit) to °C (Celsius):(a) Write the probability model for the distribution of temperature in °C in June in LA.(b) What is the probability of observing a 28°C (which roughly
Answer Preview: (a) Probability Model for Temperature in C in June in LA: Let X be the temperature in C in June in LA. We can use the given equation to convert temper…

, Chapter: 6 -Problem: 5 >> The General Social Survey asked a random sample of 1,390 Americans the following question: "On the whole, do you think it should or should not be the government's responsibility to promote equality between men and women?" 82% of the respondents said it "should be". At a 95% confidence level, this sample has 2% margin of error. Based on this information, determine if the following statements are tr
Answer Preview: (a) True: With a 95% confidence level and a 2% margin of error, we can be 95% confident that the true population proportion falls within the range of …

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, Chapter: 6 -Problem: 34 >> Microhabitat factors associated with forage and bed sites of barking deer in Hainan Island, China were examined. In this region woods make up 4.8% of the land, cultivated grass plot makes up 14.7%, and deciduous forests make up 39.6%. Of the 426 sites where the deer forage, 4 were categorized as woods, 16 as cultivated grassplot, and 61 as deciduous forests. The table below summarizes these data.(
Answer Preview: (a) Hypotheses: Null Hypothesis (H0): The distribution of barking deer foraging across different habitats is equal (no preference for any habitat). Al…

, Chapter: 5 -Problem: 11 >> A hospital administrator hoping to improve wait times decides to estimate the average emergency room waiting time at her hospital. She collects a simple random sample of 64 patients and determines the time (in minutes) between when they checked in to the ER until they were first seen by a doctor. A 95% confidence interval based on this sample is (128 minutes, 147 minutes), which is based on the no
Answer Preview: (a) True. The 95% confidence interval (128 minutes, 147 minutes) means that we are 95% confident tha…

, Chapter: 7 -Problem: 45 >> Exercise 7.31 introduced an experiment that was conducted with the goal of identifying a treatment that reduces subjects' psychopathic deviant T scores, where this score measures a person's need for control or his rebellion against control. In Exercise 7.31 you evaluated the success of each treatment individually. An alternative analysis involves comparing the success of treatments. The relevant A
Answer Preview: (a). Null Hypothesis: H o : All three treatments have similar mean T scores. H o : …

, Chapter: 6 -Problem: 27 >> The National Sleep Foundation conducted a survey on the sleep habits of randomly sampled transportation workers and a control sample of non-transportation workers. The results of the survey are shown below.Conduct a hypothesis test to evaluate if these data provide evidence of a difference between the proportions of truck drivers and non-transportation workers (the control group) who get less than
Answer Preview: To conduct a hypothesis test to evaluate if there is evidence of a difference between the proportions of truck drivers and non-transportation workers …

, Chapter: 6 -Problem: 7 >> A local news outlet reported that 56% of 600 randomly sampled Kansas residents planned to set off fireworks on July 4th. Determine the margin of error for the 56% point estimate using a 95% confidence level.
Answer Preview: To calculate the margin of error for the 56% point estimate with a 95% confidence level, you can use …

, Chapter: 5 -Problem: 3 >> As part of a quality control process for computer chips, an engineer at a factory randomly samples 212 chips during a week of production to test the current rate of chips with severe defects. She finds that 27 of the chips are defective.(a) What population is under consideration in the data set?(b) What parameter is being estimated?(c) What is the point estimate for the parameter?(d) What is the n
Answer Preview: (a) The population under consideration in the data set is the entire production of computer chips du…

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, Chapter: 6 -Problem: 46 >> A Gallup poll surveyed Americans about their employment status and whether or not they have diabetes. The survey results indicate that 1.5% of the 47,774 employed (full or part time) and 2.5% of the 5,855 unemployed 18-29 year olds have diabetes.(a) Create a two-way table presenting the results of this study. (b) State appropriate hypotheses to test for difference in proportions of diabetes betwee
Answer Preview: (a) Two-way table presenting the results of the study: Diabetes Positive No Diabetes Total Employed (18-29) 716 47,058 47,774 Unemployed (18-29) 146 5…

, Chapter: 6 -Problem: 35 >> Does being part of a support group affect the ability of people to quit smoking? A county health department enrolled 300 smokers in a randomized experiment. 150 participants were assigned to a group that used a nicotine patch and met weekly with a support group; the other 150 received the patch and did not meet with a support group. At the end of the study, 40 of the participants in the patch plus
Answer Preview: (a) Two-way table presenting the results of the study: Quit Not Quit --------------------------------------------------------- …

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, Chapter: 6 -Problem: 43 >> We are interested in estimating the proportion of students at a university who smoke. Out of a random sample of 200 students from this university, 40 students smoke.(a) Calculate a 95% confidence interval for the proportion of students at this university who smoke, and interpret this interval in context.(b) If we wanted the margin of error to be no larger than 2% at a 95% confidence level for the
Answer Preview: (a) To calculate a 95% confidence interval for the proportion of students who smoke, we can use the formula for confidence intervals of proportions. T…

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, Chapter: 5 -Problem: 16 >> Write the null and alternative hypotheses in words and using symbols for each of the following situations.(a) Since 2008, chain restaurants in California have been required to display calorie counts of each menu item. Prior to menus displaying calorie counts, the average calorie intake of diners at a restaurant was 1100 calories. After calorie counts started to be displayed on menus, a nutritionis
Answer Preview: (a) Situation: The nutritionist collected data on the number of calories consumed at a restaurant be…

, Chapter: 5 -Problem: 18 >> A study suggests that the 25% of 25 year olds have gotten married. You believe that this is incorrect and decide to collect your own sample for a hypothesis test. From a random sample of 25 year olds in census data with size 776, you find that 24% of them are married. A friend of yours offers to help you with setting up the hypothesis test and comes up with the following hypotheses. Indicate any e
Answer Preview: There is an error in the friend's formulation of the hypotheses. The correct …

, Chapter: 5 -Problem: 27 >> The General Social Survey asked the question: "After an average work day, about how many hours do you have to relax or pursue activities that you enjoy?" to a random sample of 1,155 Americans. A 95% confidence interval for the mean number of hours spent relaxing or pursuing activities they enjoy was (1.38, 1.92).(a) Interpret this interval in context of the data.(b) Suppose another set of research
Answer Preview: (a) Interpretation of the confidence interval in the context of the data: The 95% confidence interval (1 38, 1 92) means that we are 95% confident tha…

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, Chapter: 5 -Problem: 34 >> Define the term "sampling distribution" of the sample proportion, and describe how the shape, center, and spread of the sampling distribution change as the sample size increases when p = 0.1.
Answer Preview: The "sampling distribution" of the sample proportion …

, Chapter: 6 -Problem: 38 >> Lymphatic lariasis is a disease caused by a parasitic worm. Complications of the disease can lead to extreme swelling and other complications. Here we consider results from a randomized experiment that compared three dierent drug treatment options to clear people of the this parasite, which people are working to eliminate entirely. The results for  the second year of the study are given below:(a)
Answer Preview: (a) Hypotheses and Conditions: Let's set up the hypotheses for evaluating whether there is any difference in the performance of the three drug treatme…

, Chapter: 5 -Problem: 19 >> Teens were surveyed about cyberbullying, and 54% to 64% reported experiencing cyberbullying (95% confidence interval). Answer the following questions based on this interval.(a) A newspaper claims that a majority of teens have experienced cyberbullying. Is this claim supported by the confidence interval? Explain your reasoning.(b) A researcher conjectured that 70% of teens have experienced cyberbul
Answer Preview: (a) A newspaper claims that a majority of teens have experienced cyberbullying. The confidence inter…

, Chapter: 5 -Problem: 30 >> Determine if the following statements are true or false, and explain your reasoning. If false, state how it could be corrected.(a) If a given value (for example, the null hypothesized value of a parameter) is within a 95% confidence interval, it will also be within a 99% confidence interval.(b) Decreasing the significance level (?) will increase the probability of making a Type 1 Error.(c) Suppose
Answer Preview: (a) False. The statement is not necessarily true. A 95% confidence interval means that if we were to take many samples and calculate the confidence in…

, Chapter: 6 -Problem: 44 >> It believed that large doses of acetaminophen (the active ingredient in over the counter pain relievers like Tylenol) may cause damage to the liver. A researcher wants to conduct a study to estimate the proportion of acetaminophen users who have liver damage. For participating in this study, he will pay each subject $20 and provide a free medical consultation if the patient has liver damage. (a) I
Answer Preview: (a) To estimate the minimum amount of money the researcher needs to set aside to pay his subjects, we need to consider the formula for the sample size …

, Chapter: 5 -Problem: 25 >> A patient named Diana was diagnosed with Fibromyalgia, a long-term syndrome of body pain, and was prescribed anti-depressants. Being the skeptic that she is, Diana didn't initially believe that anti-depressants would help her symptoms. However after a couple months of being on the medication she decides that the anti-depressants are working, because she feels like her symptoms are in fact getting
Answer Preview: (a) Hypotheses in words for Diana's skeptical position when she started taking the anti-depressants: …

, Chapter: 6 -Problem: 40 >> The OpenIntro website occasionally experiments with design and link placement. We conducted one experiment testing three different placements of a download link for this textbook on the book's main page to see which location, if any, led to the most downloads. The number of site visitors included in the experiment was 701 and is captured in one of the response combinations in the following table:(
Answer Preview: (a) To calculate the actual number of site visitors in each of the six response categories, we can use the provided percentages and the total number of site visitors in the experiment, which is 701. L…

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, Chapter: 6 -Problem: 32 >> Determine if the statements below are true or false. For each false statement, suggest an alternative wording to make it a true statement. (a) As the degrees of freedom increases, the mean of the chisquare distribution increases. (b) If you found X2 = 10 with df = 5 you would fail to reject H0 at the 5% significance level. (c) When finding the p-value of a chi-square test, we always shade the tail
Answer Preview: (a) False. Suggested alternative wording: As the degre…

, Chapter: 7 -Problem: 3 >> An independent random sample is selected from an approximately normal population with an unknown standard deviation. Find the p-value for the given sample size and test statistic. Also determine if the null hypothesis would be rejected at ? = 0.05. (a) n = 11, T = 1.91 (b) n = 17, T = -3.45 (c) n = 7, T = 0.83 (d) n = 28, T = 2.13
Answer Preview: Let's calculate the p-value and determine whether the null hypothesis would be rejected for each case: (a) n = 11, T = 1 91 The degrees of freedom for …

, Chapter: 6 -Problem: 18 >> The Stanford University Heart Transplant Study was conducted to determine whether an experimental heart transplant program increased lifespan. Each patient entering the program was officially designated a heart transplant candidate, meaning that he was gravely ill and might benefit from a new heart. Patients were randomly assigned into treatment and control groups. Patients in the treatment group
Answer Preview: We cannot construct a confidence interval using the normal approximation in this case because the conditions for the normal approximation are not sati…

, Chapter: 6 -Problem: 21 >> Exercise 6.11 presents the results of a poll evaluating support for a generically branded "National Health Plan" in the United States. 79% of 347 Democrats and 55% of 617 Independents support a National Health Plan. (a) Calculate a 95% confidence interval for the difference between the proportion of Democrats and Independents who support a National Health Plan (pD-pI), and interpret it in this con
Answer Preview: Proportion of Democrats supporting the National Health Plan (pD) = 79% = 0 79 Proportion of Independ…

, Chapter: 5 -Problem: 36 >> Suppose you conduct a hypothesis test based on a sample where the sample size is n = 50, and arrive at a p-value of 0.08. You then refer back to your notes and discover that you made a careless mistake, the sample size should have been n = 500. Will your p-value increase, decrease, or stay the same? Explain.
Answer Preview: If you made a careless mistake and the actual sample size should have been n = 500 instead of n = 50…

, Chapter: 6 -Problem: 11 >> A Kaiser Family Foundation poll for US adults in 2019 found that 79% of Democrats, 55% of Independents, and 24% of Republicans supported a generic "National Health Plan". There were 347 Democrats, 298 Republicans, and 617 Independents surveyed. (a) A political pundit on TV claims that a majority of Independents support a National Health Plan. Do these data provide strong evidence to support this t
Answer Preview: (a) To determine if the data provide strong evidence to support the claim that a majority of Indepen…

, Chapter: 6 -Problem: 25 >> Results of a poll evaluating support for drilling for oil and natural gas off the coast of California were introduced in Exercise 6.23.(a) What percent of college graduates and what percent of the non-college graduates in this sample support drilling for oil and natural gas off the Coast of California? (b) Conduct a hypothesis test to determine if the data provide strong evidence that the proporti
Answer Preview: To calculate the percentages of college graduates and non-college graduates who support drilling for oil and natural gas off the coast of California, …

, Chapter: 5 -Problem: 22 >> 400 students were randomly sampled from a large university, and 289 said they did not get enough sleep. Conduct a hypothesis test to check whether this represents a statistically significant difference from 50%, and use a significance level of 0.01.
Answer Preview: To conduct a hypothesis test to check whether the proportion of students who did not get enough slee…

, Chapter: 6 -Problem: 47 >> Rock-paper-scissors is a hand game played by two or more people where players choose to sign either rock, paper, or scissors with their hands. For your statistics class project, you want to evaluate whether players choose between these three options randomly, or if certain options are favored above others. You ask two friends to play rock-paper-scissors and count the times each option is played. T
Answer Preview: To evaluate whether players choose between the three options of rock, paper, and scissors randomly or if certain options are favored above others, we …

, Chapter: 6 -Problem: 41 >> A local news survey asked 500 randomly sampled Los Angeles residents which shipping carrier they prefer to use for shipping holiday gifts. The table below shows the distribution of responses by age group as well as the expected counts for each cell (shown in parentheses).(a) State the null and alternative hypotheses for testing for independence of age and preferred shipping method for holiday gift
Answer Preview: (a) Null and Alternative Hypotheses: The null hypothesis (H0) states that there is no association be…

, Chapter: 6 -Problem: 20 >> The United States federal government shutdown of 2018-2019 occurred from December 22, 2018 until January 25, 2019, a span of 35 days. A Survey USA poll of 614 randomly sampled Americans during this time period reported that 48% of those who make less than $40,000 per year and 55% of those who make $40,000 or more per year said the government shutdown has not at all affected them personally. A 95%
Answer Preview: (a) True. The 95% confidence interval for (p <40K - p 40K) is (-0 16, 0 02). Since this interval doe…

, Chapter: 6 -Problem: 15 >> Exercise 6.11 presents the results of a poll evaluating support for a generic "National Health Plan" in the US in 2019, reporting that 55% of Independents are supportive. If we wanted to estimate this number to within 1% with 90% confidence, what would be an appropriate sample size? Data from Exercise 6.11A Kaiser Family Foundation poll for US adults in 2019 found that 79% of Democrats, 55% of Ind
Answer Preview: To calculate an appropriate sample size for estimating the support of a generic "National Health Pla…

, Chapter: 6 -Problem: 31 >> Determine if the statements below are true or false. For each false statement, suggest an alternative wording to make it a true statement. (a) The chi-square distribution, just like the normal distribution, has two parameters, mean and standard deviation. (b) The chi-square distribution is always right skewed, regardless of the value of the degrees of freedom parameter. (c) The chi-square statisti
Answer Preview: (a) False statement. Suggested alternative wording: The chi-square distribution has one parameter…

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, Chapter: 5 -Problem: 17 >> A study suggests that 60% of college student spend 10 or more hours per week communicating with others online. You believe that this is incorrect and decide to collect your own sample for a hypothesis test. You randomly sample 160 students from your dorm and find that 70% spent 10 or more hours a week communicating with others online. A friend of yours, who offers to help you with the hypothesis t
Answer Preview: There is a mistake in the formulation of the hypotheses. The correct hypotheses for the hypothesis …

, Chapter: 6 -Problem: 3 >> Suppose that 90% of orange tabby cats are male. Determine if the following statements are true or false, and explain your reasoning. (a) The distribution of sample proportions of random samples of size 30 is left skewed. (b) Using a sample size that is 4 times as large will reduce the standard error of the sample proportion by one-half. (c) The distribution of sample proportions of random samples
Answer Preview: To answer these statements, we need to understand some concepts related to sample proportions and their distributions. Let's assume we have a populati…

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, Chapter: 5 -Problem: 15 >> Write the null and alternative hypotheses in words and then symbols for each of the following situations.(a) A tutoring company would like to understand if most students tend to improve their grades (or not) after they use their services. They sample 200 of the students who used their service in the past year and ask them if their grades have improved or declined from the previous year.(b) Employe
Answer Preview: (a) Null Hypothesis (H0): The tutoring company's services have no effect on students' grades; there …

, Chapter: 5 -Problem: 10 >> A poll conducted in 2013 found that 52% of U.S. adult Twitter users get at least some news on Twitter, and the standard error for this estimate was 2.4%. Identify each of the following statements as true or false. Provide an explanation to justify each of your answers.(a) The data provide statistically significant evidence that more than half of U.S. adult Twitter users get some news through Twitt
Answer Preview: (a) True: To determine whether the data provides statistically significant evidence that more than half of U S. adult Twitter users get some news thro…

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, Chapter: 5 -Problem: 31 >> A USA Today/Gallup poll asked a group of unemployed and underemployed Americans if they have had major problems in their relationships with their spouse or another close family member as a result of not having a job (if unemployed) or not having a full-time job (if underemployed). 27% of the 1,145 unemployed respondents and 25% of the 675 underemployed respondents said they had major problems in r
Answer Preview: (a) Hypotheses for evaluating if the proportions of unemployed and underemployed people who had relationship problems were different: Null Hypothesis …

, Chapter: 6 -Problem: 1 >> Suppose that 8% of college students are vegetarians. Determine if the following statements are true or false, and explain your reasoning.(a) The distribution of the sample proportions of vegetarians in random samples of size 60 is approximately normal since n ? 30.(b) The distribution of the sample proportions of vegetarian college students in random samples of size 50 is right skewed.(c) A random
Answer Preview: (a) True. The distribution of sample proportions of vegetarians in random samples of size 60 is approximately normal since n 30. According to the Cent…

, Chapter: 6 -Problem: 10 >> The General Social Survey asked 1,578 US residents: "Do you think the use of marijuana should be made legal, or not?" 61% of the respondents said it should be made 13 legal.  (a) Is 61% a sample statistic or a population parameter? Explain. (b) Construct a 95% confidence interval for the proportion of US residents who think marijuana should be made legal, and interpret it in the context of the dat
Answer Preview: (a) Is 61% a sample statistic or a population parameter? Explain. 61% is a sample statistic. A sample statistic is a numerical measure calculated from …

, Chapter: 6 -Problem: 12 >> Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.(a) A newspaper article states that only a minority of the Americans who decide not to go to college do so because they cannot afford it and uses the point estimate from this survey a
Answer Preview: (a) To conduct a hypothesis test to determine if the data provide strong evidence supporting the statement that only a minority of Americans who decid…

, Chapter: 7 -Problem: 9 >> You are given the following hypotheses:We know that the sample standard deviation is 8 and the sample size is 20. For what sample mean would the p-value be equal to 0.05? Assume that all conditions necessary for inference are satisfied. Transcribed Image Text: Ho : ? = 60 Ha : ? # 60
Answer Preview: To find the sample mean for which the p-value is equal to 0 05, we need to conduct a one-sample t-te…

, Chapter: 7 -Problem: 5 >> A 95% confidence interval for a population mean, , is given as (18.985, 21.015). This confidence interval is based on a simple random sample of 36 observations. Calculate the sample mean and standard deviation. Assume that all conditions necessary for inference are satisfied. Use the t-distribution in any calculations.
Answer Preview: In a 95% confidence interval for a population mean, the range between the lower and upper bounds represents the likely range for the true population m…

, Chapter: 6 -Problem: 16 >> As discussed in Exercise 6.10, the General Social Survey reported a sample where about 61% of US residents thought marijuana should be made legal. If we wanted to limit the margin of error of a 95% confidence interval to 2%, about how many Americans would we need to survey? Data from Exercise 6.10The General Social Survey asked 1,578 US residents: "Do you think the use of marijuana should be made
Answer Preview: To calculate the sample size needed to limit the margin of error of a 95% confidence interval …

, Chapter: 5 -Problem: 37 >> A study examined the average pay for men and women entering the workforce as doctors for 21 different positions.(a) If each gender was equally paid, then we would expect about half of those positions to have men paid more than women and women would be paid more than men in the other half of positions. Write appropriate hypotheses to test this scenario. (b) Men were, on average, paid more in 19 of
Answer Preview: (a) Appropriate hypotheses to test the scenario of equal pay between genders: Null Hypothesis (H0): …

, Chapter: 7 -Problem: 1 >> An independent random sample is selected from an approximately normal population with unknown standard deviation. Find the degrees of freedom and the critical t-value (t*) for the given sample size and confidence level. (a) n = 6, CL = 90% (b) n = 21, CL = 98% (c) n = 29, CL = 95% (d) n = 12, CL = 99%
Answer Preview: To find the degrees of freedom (df) and the critical t-value (t*) for the given sample size and conf…

, Chapter: 5 -Problem: 33 >> The nutrition label on a bag of potato chips says that a one ounce (28 gram) serving of potato chips has 130 calories and contains ten grams of fat, with three grams of saturated fat. A random sample of 35 bags yielded a confidence interval for the number of calories per bag of 128.2 to 139.8 calories. Is there evidence that the nutrition label does not provide an accurate measure of calories in t
Answer Preview: To determine whether there is evidence that the nutrition label does not provide an accurate measure of calories in the bags of potato chips, we can p…

, Chapter: 7 -Problem: 10 >> For a given confidence level, t*df is larger than z*. Explain how t*df being slightly larger than z* affects the width of the confidence interval.
Answer Preview: The terms "tdf" and "z" refer to critical values from different distributions used in constructing confidence intervals. t*df: This represents the cri…

, Chapter: 6 -Problem: 48 >> On June 28, 2012 the U.S. Supreme Court upheld the much debated 2010 healthcare law, declaring it constitutional. A Gallup poll released the day after this decision indicates that 46% of 1,012 Americans agree with this decision. At a 95% confidence level, this sample has a 3% margin of error. Based on this information, determine if the following statements are true or false, and explain your reaso
Answer Preview: (a) True: The statement is true. Given a 95% confidence level and a 3% margin of error, we can const…

, Chapter: 6 -Problem: 23 >> A survey asked 827 randomly sampled registered voters in California "Do you support? Or do you oppose? Drilling for oil and natural gas off the Coast of California? Or do you not know enough to say?" Below is the distribution of responses, separated based on whether or not the respondent graduated from college.(a) What percent of college graduates and what percent of the non-college graduates in t
Answer Preview: (a) To determine the percent of college graduates and non-college graduates who do not know enough to have an opinion on drilling for oil and natural …

, Chapter: 6 -Problem: 9 >> A survey on 1,509 high school seniors who took the SAT and who completed an optional web survey shows that 55% of high school seniors are fairly certain that they will participate in a study abroad program in college. (a) Is this sample a representative sample from the population of all high school seniors in the US? Explain your reasoning. (b) Let's suppose the conditions for inference are met. E
Answer Preview: (a) No, this sample may not be representative of all high school seniors in the US. The survey was conducted among high school seniors who took the SA…

, Chapter: 6 -Problem: 30 >> A physical education teacher at a high school wanting to increase awareness on issues of nutrition and health asked her students at the beginning of the semester whether they believed the expression "an apple a day keeps the doctor away", and 40% of the students responded yes. Throughout the semester she started each class with a brief discussion of a study highlighting positive effects of eating
Answer Preview: No, the physical education teacher cannot use the two-proportion method from this section for this a…

, Chapter: 7 -Problem: 22 >> We considered the differences between the reading and writing scores of a random sample of 200 students who took the High School and Beyond Survey in Exercise 7.20. The mean and standard deviation of the differences are x?read-write = -0.545 and 8.887 points. (a) Calculate a 95% confidence interval for the average difference between the reading and writing scores of all students. (b) Interpret thi
Answer Preview: Let's proceed with the calculations: (a) 95% Confidence Interval: The formula for calculating the confidence interval for the mean is: Confidence Inte…

, Chapter: 5 -Problem: 9 >> In 2013, the Pew Research Foundation reported that "45% of U.S. adults report that they live with one or more chronic conditions", and the standard error for this estimate is 1.2%. Identify each of the following statements as true or false. Provide an explanation to justify each of your answers.(a) We can say with certainty that the confidence interval from Exercise 5.7 contains the true percentag
Answer Preview: To create a 95% confidence interval for the proportion of U S. adults who live with one or more chronic conditions, we'll use the information provided…

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, Chapter: 5 -Problem: 32 >> It is believed that nearsightedness affects about 8% of all children. In a random sample of 194 children, 21 are nearsighted. Conduct a hypothesis test for the following question: do these data provide evidence that the 8% value is inaccurate?
Answer Preview: To conduct a hypothesis test to determine whether the 8% value is inaccurate, we can use a significa…

, Chapter: 6 -Problem: 8 >> Greece has faced a severe economic crisis since the end of 2009. A Gallup poll surveyed 1,000 randomly sampled Greeks in 2011 and found that 25% of them said they would rate their lives poorly enough to be considered "suffering". (a) Describe the population parameter of interest. What is the value of the point estimate of this parameter? (b) Check if the conditions required for constructing a conf
Answer Preview: (a) Population parameter of interest: The population parameter of interest in this case is the proportion of all Greeks who would rate their lives poorly enough to be considered "suffering". Point est…

, Chapter: 4 -Problem: 38 >> Exercise 4.36 states that the distribution of speeds of cars traveling on the Interstate 5 Freeway (I-5) in California is nearly normal with a mean of 72.6 miles/hour and a standard deviation of 4.78 miles/hour. The speed limit on this stretch of the I-5 is 70 miles/hour.(a) A highway patrol officer is hidden on the side of the freeway. What is the probability that 5 cars pass and none are speedin
Answer Preview: To solve this problem, we'll use the concept of the normal distribution and the properties of probability and expected value. Given data: Mean speed (…

, Chapter: 5 -Problem: 23 >> You are given the following hypotheses:We know the sample size is 90. For what sample proportion would the p-value be equal to 0.05? Assume that all conditions necessary for inference are satisfied. Transcribed Image Text: Ho: p = 0.3 HA : p + 0.3
Answer Preview: To find the sample proportion for which the p-value would be equal to 0 05, we need to perform a hyp…

, Chapter: 4 -Problem: 22 >> A Gallup Poll found that 7% of teenagers (ages 13 to 17) suffer from arachnophobia and are extremely afraid of spiders. At a summer camp there are 10 teenagers sleeping in each tent. Assume that these 10 teenagers are independent of each other.(a) Calculate the probability that at least one of them suffers from arachnophobia.(b) Calculate the probability that exactly 2 of them suffer from arachnop
Answer Preview: To solve this problem, we can use the binomial probability formula: P(X = k) = (n C k) * p^k * (1 - …

, Chapter: 5 -Problem: 24 >> You are given the following hypotheses:We know that the sample size is 1,429. For what sample proportion would the p-value be equal to 0.01? Assume that all conditions necessary for inference are satisfied. Transcribed Image Text: Ho p = 0.9 HA: P = 0.9
Answer Preview: To calculate the sample proportion for which the p-value is equal to 0 01, we ne…

, Chapter: 1 -Problem: 20 >> On a large college campus first-year students and sophomores live in dorms located on the eastern part of the campus and juniors and seniors live in dorms located on the western part of the campus. Suppose you want to collect student opinions on a new housing structure the college administration is proposing and you want to make sure your survey equally represents opinions from students from all y
Answer Preview: (a) This type of study is a stratified sampling study. (b) To carry out this study using stratified …

, Chapter: 7 -Problem: 4 >> An independent random sample is selected from an approximately normal population with an unknown standard deviation. Find the p-value for the given sample size and test statistic. Also determine if the null hypothesis would be rejected at a = 0.01. (a) n = 26, T = 2.485 (b) n = = 18, T = 0.5
Answer Preview: To find the p-value and determine if the null hypothesis would be rejected at a significance level o…

, Chapter: 3 -Problem: 11 >> The table below shows the distribution of education level attained by US residents by gender based on data collected in the 2010 American Community Survey(a) What is the probability that a randomly chosen man has at least a Bachelor's degree?(b) What is the probability that a randomly chosen woman has at least a Bachelor's degree?(c) What is the probability that a man and a woman getting married b
Answer Preview: (a) Probability that a randomly chosen man has at least a Bachelor's degree: To find this probabilit…

, Chapter: 5 -Problem: 13 >> A website is trying to increase registration for first-time visitors, exposing 1% of these visitors to a new site design. Of 752 randomly sampled visitors over a month who saw the new design, 64 registered.(a) Check any conditions required for constructing a confidence interval.(b) Compute the standard error.(c) Construct and interpret a 90% confidence interval for the fraction of first-time visit
Answer Preview: (a) Conditions required for constructing a confidence interval: Random sampling: The visitors must be randomly sampled to ensure that the sample is re…

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, Chapter: 5 -Problem: 5 >> A nonprofit wants to understand the fraction of households that have elevated levels of lead in their drinking water. They expect at least 5% of homes will have elevated levels of lead, but not more than about 30%. They randomly sample 800 homes and work with the owners to retrieve water samples, and they compute the fraction of these homes with elevated lead levels. They repeat this 1,000 times a
Answer Preview: (a) The distribution built from repeating the process 1,000 times and collecting sample proportions …

, Chapter: 5 -Problem: 28 >> In Exercise 5.21, we learned that a Rasmussen Reports survey of 1,000 US adults found that 42% believe raising the minimum wage will help the economy. Construct a 99% confidence interval for the true proportion of US adults who believe this. Data from Exercise 5.21Do a majority of US adults believe raising the minimum wage will help the economy, or is there a majority who do not believe this? A Ra
Answer Preview: To construct a 99% confidence interval for the true proportion of US adults who believe raising the …

, Chapter: 7 -Problem: 6 >> A 90% confidence interval for a population mean is (65, 77). The population distribution is approximately normal and the population standard deviation is unknown. This confidence interval is based on a simple random sample of 25 observations. Calculate the sample mean, the margin of error, and the sample standard deviation.
Answer Preview: To calculate the sample mean, margin of error, and sample standard deviation, we can use the informa…

, Chapter: 5 -Problem: 35 >> Determine whether the following statement is true or false, and explain your reasoning: "With large sample sizes, even small differences between the null value and the observed point estimate can be statistically significant."
Answer Preview: The statement is generally true. In hypothesis testing, the term "statistically significant" refers …

, Chapter: 6 -Problem: 2 >> About 77% of young adults think they can achieve the American dream. Determine if the following statements are true or false, and explain your reasoning.(a) The distribution of sample proportions of young Americans who think they can achieve the American dream in samples of size 20 is left skewed. (b) The distribution of sample proportions of young Americans who think they can achieve the American
Answer Preview: To determine the truth of the statements, we need to consider the properties of sample proportions and their distributions. (a) The distribution of sa…

, Chapter: 5 -Problem: 8 >> A poll conducted in 2013 found that 52% of U.S. adult Twitter users get at least some news on Twitter. The standard error for this estimate was 2.4%, and a normal distribution may be used to model the sample proportion. Construct a 99% confidence interval for the fraction of U.S. adult Twitter users who get some news on Twitter, and interpret the confidence interval in context.
Answer Preview: To construct a 99% confidence interval for the fraction of U S. adult Twitter users who get some new…

, Chapter: 6 -Problem: 28 >> Researchers studying the link between prenatal vitamin use and autism surveyed the mothers of a random sample of children aged 24 - 60 months with autism and conducted another separate random sample for children with typical development. The table below shows the number of mothers in each group who did and did not use prenatal vitamins during the three months before pregnancy (periconceptional per
Answer Preview: (a) Hypotheses: Let's assume that the use of prenatal vitamins and the occurrence of autism are independent of each other. We can state the null and a…

, Chapter: 5 -Problem: 7 >> In 2013, the Pew Research Foundation reported that "45% of U.S. adults report that they live with one or more chronic conditions". However, this value was based on a sample, so it may not be a perfect estimate for the population parameter of interest on its own. The study reported a standard error of about 1.2%, and a normal model may reasonably be used in this setting. Create a 95% confidence int
Answer Preview: To create a 95% confidence interval for the proportion of U S. adults who live with one or more chro…

, Chapter: 5 -Problem: 12 >> The General Social Survey asked the question: "For how many days during the past 30 days was your mental health, which includes stress, depression, and problems with emotions, not good?" Based on responses from 1,151 US residents, the survey reported a 95% confidence interval of 3.40 to 4.24 days in 2010.(a) Interpret this interval in context of the data.(b) What does "95% confident" mean? Explain
Answer Preview: (a) Interpretation of the 95% confidence interval in context of the data: The 95% confidence interva…

, Chapter: 5 -Problem: 29 >> A food safety inspector is called upon to investigate a restaurant with a few customer reports of poor sanitation practices. The food safety inspector uses a hypothesis testing framework to evaluate whether regulations are not being met. If he decides the restaurant is in gross violation, its license to serve food will be revoked.(a) Write the hypotheses in words.(b) What is a Type 1 Error in this
Answer Preview: (a) Hypotheses in words: Null Hypothesis (H0): The restaurant is not in gross violation of food safety regulations. Alternative Hypothesis (Ha): The restaurant is in gross violation of food safety reg…

, Chapter: 6 -Problem: 29 >> In July 2008 the US National Institutes of Health announced that it was stopping a clinical study early because of unexpected results. The study population consisted of HIV-infected women in sub-Saharan Africa who had been given single dose Nevaripine (a treatment for HIV) while giving birth, to prevent transmission of HIV to the infant. The study was a randomized comparison of continued treatment
Answer Preview: (a) Two-way table presenting the results of the study: Virologic Failure No Virologic Failure ------…

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, Chapter: 5 -Problem: 20 >> Exercise 5.11 provides a 95% confidence interval for the mean waiting time at an emergency room (ER) of (128 minutes, 147 minutes). Answer the following questions based on this interval.(a) A local newspaper claims that the average waiting time at this ER exceeds 3 hours. Is this claim supported by the confidence interval? Explain your reasoning.(b) The Dean of Medicine at this hospital claims the
Answer Preview: (a) A local newspaper claims that the average waiting time at this ER exceeds 3 hours. The 95% confi…

, Chapter: 6 -Problem: 39 >> A teacher wanting to increase the active learning component of her course is concerned about student reactions to changes she is planning to make. She conducts a survey in her class, asking students whether they believe more active learning in the classroom (hands on exercises) instead of traditional lecture will helps improve their learning. She does this at the beginning and end of the semester
Answer Preview: The methods typically covered in a chapter on data analysis might include techniques for descriptive statistics, hypothesis testing, and inferential s…

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, Chapter: 2 -Problem: 30 >> The statistic x/median can be used as a measure of skewness. Suppose we have a distribution where all observations are greater than 0, xi > 0. What is the expected shape of the distribution under the following conditions? Explain your reasoning.(a) (x/median) = 1(b) (x/median) < 1(c) (x/median) > 1
Answer Preview: The statistic x/median can indeed be used as a measure of skewness, particularly when dealing with distributions where all observations are greater th…

, Chapter: 4 -Problem: 20 >> We learned in Exercise 4.18 that about 90% of American adults had chickenpox before adulthood. We now consider a random sample of 120 American adults.(a) How many people in this sample would you expect to have had chickenpox in their childhood? And with what standard deviation?(b) Would you be surprised if there were 105 people who have had chickenpox in their childhood?(c) What is the probability
Answer Preview: To answer these questions, we can use the binomial distribution, as the situation involves a random sample of American adults, and each adult either h…

, Chapter: 3 -Problem: 33 >> A portfolio's value increases by 18% during a nancial boom and by 9% during normal times. It decreases by 12% during a recession. What is the expected return on this portfolio if each scenario is equally likely?
Answer Preview: To calculate the expected return of the portfolio, we need to find the average return across all the …

, Chapter: 4 -Problem: 35 >> In the game of roulette, a wheel is spun and you place bets on where it will stop. One popular bet is that it will stop on a red slot; such a bet has an 18/38 chance of winning. If it stops on red, you double the money you bet. If not, you lose the money you bet. Suppose you play 3 times, each time with a $1 bet. Let Y represent the total amount won or lost. Write a probability model for Y.
Answer Preview: To write a probability model for Y, we need to consider all possible outcomes of the three spins of the roulette wheel and their associated probabilit…

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