8.17 What's wrong

Explain what is wrong with each of the following.

8.18 What's wrong

Explain what is wrong with each of the following.

8.19 Draw some pictures

Consider the binomial setting with and .

8.20 Smartphones and purchases

A Google research study asked 5013 smartphone users about how they used their phones. In response to a question about purchases, 2657 reported that they purchased an item after using their smartphone to search for information about the item.⁶

8.21 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.⁷

8.22 Nonconforming switches

In Example 5.5 (pages 247–248), we calculated some binomial probabilities for inspection of a batch of switches from a large shipment of switches. Suppose that in an SRS of 150 switches, we have 10 failures.

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8.23 Significance test for nonconforming switches.

Refer to the previous exercise. In Example 5.5 (pages 247–248), we assumed that the proportion of nonconforming switches in the large shipment was 8%.

8.24 Customer preferences for your new product.

A sample of 50 potential customers was asked to use your new product and the product of the leading competitor. After one week, they were asked to indicate which product they preferred. In the sample, 30 potential customers said that they preferred your product.

8.25 How many potential customers should you sample?

Refer to the previous exercise. If you want the 95% margin of error to be 0.06 or less, what would you choose for a sample size? Explain how you calculated your answer and show your work.

8.26 How much influence do social media have on purchasing decisions?

A Gallup poll asked this question of 18,525 U.S. adults aged 18 and older.⁸ The response “No influence at all” was given by 62% of the respondents. Find a 99% confidence for the true proportion of U.S. adults who would choose “No influence at all” as their response.

8.27 Canadian teens pay to download music.

A survey of 416 Canadian teens aged 12 to 17 years were asked about downloading music from the Internet.⁹ Of these, 316 reported that they have used a fee-based website for their downloads.

8.28 Country food and Inuits.

Country food includes seal, caribou, whale, duck, fish, and berries and is an important part of the diet of the aboriginal people called Inuits, who inhabit Inuit Nunaat, the northern region of what is now called Canada. A survey of Inuits in Inuit Nunaat reported that 3274 out of 5000 respondents said that at least half of the meat and fish that they eat is country food.¹⁰ Find the sample proportion and a 95% confidence interval for the population proportion of Inuits who eat meat and fish that are at least half country food.

8.29 Mathematician tosses 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.

8.30 “Guitar Hero” and “Rock Band.”

An electronic survey of 7061 game players of “Guitar Hero” and “Rock Band” reported that 67% of players of these games who do not currently play a musical instrument said that they are likely to begin playing a real musical instrument in the next two years.¹¹ The reports describing the survey do not give the number of respondents who do not currently play a musical instrument.

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8.31 “Guitar Hero” and “Rock Band.”

Refer to the previous exercise.

8.32 Students doing community service

In a sample of 116,250 first-year college students, the National Survey of Student Engagement reported that 43% participated in community service or volunteer work.¹²

8.33 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, 43% of first-year students reported that they plan to study abroad.

8.34 How would the confidence interval change?

Refer to Exercise 8.32. Would a 90% confidence interval be wider or narrower than the one that you found in that exercise? Verify your results by computing the interval.

8.35 How would the confidence interval change?

Refer to Exercise 8.32. Would a 95% confidence interval be wider or narrower than the one that you found in that exercise? Verify your results by computing the interval.

8.36 Can we use th test?

In each of the following cases, is the sample large enough to permit safe use of the test? (The population is very large.)

8.37 Shipping the orders on time.

As part of a quality improvement program, your mail-order company is studying the process of filling customer orders. According to company standards, an order is shipped on time if it is sent within two working days of the time it is received. You select an SRS of 100 of the 6000 orders received in the past month for an audit. The audit reveals that 87 of these orders were shipped on time. Find a 95% confidence interval for the true proportion of the month's orders that were shipped on time.

8.38 Instant versus fresh-brewed coffee.

A matched pairs experiment compares the taste of instant coffee 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 50 subjects who participate in the study, 19 prefer the instant coffee and the other 31 prefer fresh-brewed. Take to be the proportion of the population that prefers fresh-brewed coffee.

8.39 Checking the demographics of a sample.

CASE 8.2 Of the 500 households that responded to the Christmas tree marketing survey, 38% were from rural areas (including small towns), and the other 62% were from urban areas (including suburbs). According to the census, 36% of Indiana households are in rural areas, and the remaining 64% are in urban areas. Let be the proportion of rural respondents. Set up hypotheses about , and perform a test of significance to examine how well the sample represents the state in regard to rural versus urban residence. Summarize your results.

8.40 More on demographics.

CASE 8.2 In the previous exercise, we arbitrarily chose to state the hypotheses in terms of the proportion of rural respondents. We could as easily have used the proportion of urban respondents.

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8.41 High-income households on a mailing list

Land's Beginning sells merchandise through the mail. It is considering buying a list of addresses from a magazine. The magazine claims that at least 30% of its subscribers have high incomes (that is, household income in excess of $120,000). Land's Beginning would like to estimate the proportion of high-income people on the list. Verifying income is difficult, but another company offers this service. Land's Beginning will pay to verify the incomes of an SRS of people on the magazine's list. They would like the margin of error of the 95% confidence interval for the proportion to be 0.04 or less. Use the guessed value to find the required sample size.

8.42 Change the specs

Refer to the previous exercise. For each of the following variations on the design specifications, state whether the required sample size will be larger, smaller, or the same as that found in Exercise 8.41.

8.43 Be an entrepreneur:

A student organization wants to start a nightclub for students under the age of 21. To assess support for this proposal, the organization will select an SRS of students and ask each respondent if he or she would patronize this type of establishment. About 70% of the student body are expected to respond favorably.

8.44 Are the customers dissatisfied?

A cell phone manufacturer would like to know what proportion of its customers are dissatisfied with the service received from their local distributor. The customer relations department will survey a random sample of customers and compute a 95% confidence interval for the proportion that are dissatisfied. From past studies, the department believes that this proportion will be about 0.09.

8.45 Increase student fees?

You have been asked to survey students at a large college to determine the proportion that favor an increase in student fees to support an expansion of the student newspaper. Each student will be asked whether he or she is in favor of the proposed increase. Using records provided by the registrar, you can select a random sample of students from the college. After careful consideration of your resources, you decide that it is reasonable to conduct a study with a sample of 200 students.

8.46 Justify the cost of the survey.

A former editor of the student newspaper agrees to underwrite the study in the previous exercise because she believes the results will demonstrate that most students support an increase in fees. She is willing to provide funds for a sample of size 400. Write a short summary for your benefactor of why the increased sample size will provide better results.

8.47 Are the customers dissatisfied?

Refer to Exercise 8.44, where you computed the sample size based on the width of a confidence interval. Now we will use the same setting to determine the sample size based on a significance test. You want to test the null hypothesis that the population proportion is 0.09 using a two-sided test with and 80% power. Use 0.19 as the proportion for the alternative. What sample size would you recommend? Note that you need to specify an alternative hypothesis to answer this question.

8.48 Nonconforming switches?

Refer to Exercises 8.22 and 8.23, where you found a confidence interval and performed a significance test for nonconforming switches. Find the sample size needed for testing the null hypothesis that the population proportion is 0.08 versus the one-sided alternative that the population proportion is greater than 0.08. Use , 80% power, and 0.20 as the alternative for your calculations.