8.14 How did you use your cell phone? A Pew Internet poll asked cell phone owners about how they used their cell phones. One question asked whether or not during the past 30 days they had used their phone while in a store to call a friend or family member for advice about a purchase they were considering. The poll surveyed 1003 adults living in the United States by telephone. Of these, 462 responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering.⁷

8.15 Do you eat breakfast? A random sample of 300 students from your college is asked if they regularly eat breakfast. One hundred and nine students responded that they did eat breakfast regularly.

8.16 Would you recommend the service to a friend? An automobile dealership asks all its customers who used its service department in a given two-week period if they would recommend the service to a friend. A total of 250 customers used the service during the two-week period, and 210 said that they would recommend the service to a friend.

8.17 How did you use your cell phone? Refer to Exercise 8.14.

8.18 Do you eat breakfast? Refer to Exercise 8.15.

8.19 Would you recommend the service to a friend? Refer to Exercise 8.16.

8.20 Whole grain versus regular grain? A study of young children was designed to increase their intake of whole-grain, rather than regular-grain, snacks. At the end of the study, the 86 children who participated in the study were presented with a choice between a regular-grain snack and a whole-grain alternative. The whole-grain alternative was chosen by 48 children. You want to examine the possibility that the children are equally likely to choose each type of snack.

8.21 Find the sample size. You are planning a survey similar to the one about cell phone use described in Exercise 8.14. You will report your results with a large-sample confidence interval. How large a sample do you need to be sure that the margin of error will not be greater than 0.05? Show your work.

8.22 What’s wrong? Explain what is wrong with each of the following:

8.23 What’s wrong? Explain what is wrong with each of the following:

8.24 Draw some pictures. Consider the binomial setting with n = 800 and p = 0.3.

8.25 Country food and Inuits. Country food includes seals, caribou, whales, ducks, fish, and berries and is an important part of the diet of the aboriginal people called Inuits who inhabit Inuit Nunangat, the northern region of what is now called Canada. A survey of Inuits in Inuit Nunangat reported that 3274 out of 5000 respondents said that at least half of the meat and fish that they eat is country food.⁸ Find the sample proportion and a 95% confidence interval for the population proportion of Inuits whose meat and fish consumption consists of at least half country food.

8.26 Soft drink consumption in New Zealand. A survey commissioned by the Southern Cross Healthcare Group reported that 16% of New Zealanders consume five or more servings of soft drinks per week. The data were obtained by an online survey of 2006 randomly selected New Zealanders over 15 years of age.⁹

8.27 Violent video games. A survey of 1050 parents who have a child under the age of 18 living at home asked about their opinions regarding violent video games. A report describing the results of the survey stated that 89% of parents say that violence in today’s video games is a problem.¹⁰

8.28 Bullying. Refer to the previous exercise. The survey also reported that 93% of the parents surveyed said that bullying contributes to violence in the United States. Answer the questions in the previous exercise for this item on the survey.

8.29 and the Normal distribution. Consider the binomial setting with n = 40. You are testing the null hypothesis that p = 0.4 versus the two-sided alternative with a 5% chance of rejecting the null hypothesis when it is true.

8.30 Students doing community service. In a sample of 159,949 first-year college students, the National Survey of Student Engagement reported that 39% participated in community service or volunteer work.¹¹

8.31 Plans to study abroad. The survey described in the previous exercise also asked about items related to academics. In response to one of these questions, 42% of first-year students reported that they plan to study abroad.

8.32 Student credit cards. In a survey of 1430 undergraduate students, 1087 reported that they had one or more credit cards.¹² Give a 95% confidence interval for the proportion of all college students who have at least one credit card.

8.33 How many credit cards? The summary of the survey described in the previous exercise reported that 43% of undergraduates had four or more credit cards. Give a 95% confidence interval for the proportion of all college students who have four or more credit cards.

8.34 How would the confidence interval change? Refer to Exercise 8.33.

8.35 Do students report Internet sources? The National Survey of Student Engagement found that 87% of students report that their peers at least “sometimes” copy information from the Internet in their papers without reporting the source.¹³ Assume that the sample size is 430,000.

8.36 Can we use the z test? In each of the following cases, state whether or not the Normal approximation to the binomial should be used for a significance test on the population proportion p. Explain your answers.

8.37 Long sermons. The National Congregations Study collected data in a one-hour interview with a key informant—that is, a minister, priest, rabbi, or other staff person or leader.¹⁴ One question concerned the length of the typical sermon. For this question, 390 out of 1191 congregations reported that the typical sermon lasted more than 30 minutes.

8.38 Instant versus fresh-brewed coffee. A matched pairs experiment compares the taste of instant with fresh-brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers. Of the 60 subjects who participate in the study, 21 prefer the instant coffee. Let p be the probability that a randomly chosen subject prefers fresh-brewed coffee to instant coffee. (In practical terms, p is the proportion of the population who prefer fresh-brewed coffee.)

8.39 Tossing a coin 10,000 times! The South African mathematician John Kerrich, while a prisoner of war during World War II, tossed a coin 10,000 times and obtained 5067 heads.

8.40 Is there interest in a new product? One of your employees has suggested that your company develop a new product. You decide to take a random sample of your customers and ask whether or not there is interest in the new product. The response is on a 1 to 5 scale with 1 indicating “definitely would not purchase”; 2, “probably would not purchase”; 3, “not sure”; 4, “probably would purchase”; and 5, “definitely would purchase.” For an initial analysis, you will record the responses 1, 2, and 3 as No and 4 and 5 as Yes. What sample size would you use if you wanted the 95% margin of error to be 0.25 or less?

8.41 More information is needed. Refer to the previous exercise. Suppose that after reviewing the results of the previous survey, you proceeded with preliminary development of the product. Now you are at the stage where you need to decide whether or not to make a major investment to produce and market it. You will use another random sample of your customers, but now you want the margin of error to be smaller. What sample size would you use if you wanted the 95% margin of error to be 0.015 or less?

8.42 Sample size needed for an evaluation. You are planning an evaluation of a semester-long alcohol awareness campaign at your college. Previous evaluations indicate that about 20% of the students surveyed will respond Yes to the question “Did the campaign alter your behavior toward alcohol consumption?” How large a sample of students should you take if you want the margin of error for 95% confidence to be about 0.07?

8.43 Sample size needed for an evaluation, continued. The evaluation in the previous exercise will also have questions that have not been asked before, so you do not have previous information about the possible value of p. Repeat the preceding calculation for the following values of p*: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9. Summarize the results in a table and graphically. What sample size will you use?

8.44 Are the customers dissatisfied? An automobile manufacturer would like to know what proportion of its customers are dissatisfied with the service received from their local dealer. The customer relations department will survey a random sample of customers and compute a 95% confidence interval for the proportion who are dissatisfied. From past studies, it believes that this proportion will be about 0.25. Find the sample size needed if the margin of error of the confidence interval is to be no more than 0.035.

8.45 Sample size for coffee. Refer to Exercise 8.38 where we analyzed data from a matched pairs study that compared preferences for instant versus fresh-brewed coffee. Suppose that you want to design a similar study. The null hypothesis is that instant and fresh-brewed are equally likely to be preferred and the alternative is two-sided. You will use α = 0.05. What is the sample size needed to detect a preference of 60% for fresh-brewed with 0.80 probability?

8.46 Sample size for tossing a coin. Refer to Exercise 8.39 where we analyzed the 10,000 coin tosses made by John Kerrich. Suppose that you want to design a study that would test the hypothesis that a coin is fair versus the alternative that the probability of a head is 0.51. Using a two-sided test with α = 0.05. what sample size would be needed to have 0.80 power to detect this alternative?