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Chapter 8: Q 65. (page 542)

Check them all Determine if the conditions are met for constructing a confidence interval for the population mean in each of the following settings.

a. How much time do students at your school spend on the Internet? You collect data from the 32members of your AP Statistics class and calculate the mean amount of time that these students spent on the Internet yesterday.

b. Is the real-estate market heating up? To estimate the mean sales price, a realtor in a large city randomly selected 100home sales from the previous 6months in her city. These sales prices are displayed in the boxplot.

Short Answer

Expert verified

a. Random Sample condition is not met.

b. All conditions are satisfied.

Step by step solution

01

Part (a) Step 1: Given Information

It is given that n=32

Population is of all students.

02

Part (a) Step 2: Explanation

Random: AP Statistics is chosen as per requirement. It can never be random sample.

Less than 10%of population: 32students are less than 10%of students. This condition is not satisfied.

Sample Size: 32>30, sample size is larger. Condition of large sample size is satisfied.

Condition of Random sample is not met.

03

Part (b) Step 1: Given Information

It is given that n=100

Population is of all home sales in city.

04

Part (b) Step 2: Explanation

Random: Home sales are to be selected randomly. Hence, this condition is satisfied.

Less than 10% of population: 100<10%of all population. This is also satisfied.

Large Sample Size: 100>30, this condition is also met.

All conditions are satisfied.

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Most popular questions from this chapter

Age and video games Refer to Exercise 41. The study also estimated that 67% of adults aged 18鈥�29play video games, but only 25%of adults aged 65and older play video games.

a. Explain why you do not have enough information to give confidence intervals for these two age groups separately.

b. Do you think a 95% confidence interval for adults aged 18鈥�29 would have a larger or smaller margin of error than the estimate from Exercise 41? Explain your answer.

A newspaper reporter asked an SRS of 100residents in a large city for their opinion about the mayor鈥檚 job performance. Using the results from the sample, the C%confidence interval for the proportion of all residents in the city who approve of the mayor鈥檚 job performance is 0.565to0.695. What is the value of C?

a. 82

b. 86

c. 90

d. 95

e. 99

Power lines and cancer Does living near power lines cause leukemia in

children? The National Cancer Institute spent 5years and $5million gathering data on this question. The researchers compared 638children who had leukemia with 620who did not. They went into the homes and measured the magnetic fields in children鈥檚 bedrooms, in other rooms, and at the front door. They recorded facts about power lines near the family home and also near the mother鈥檚 residence when she was pregnant. Result: No association between leukemia and exposure to magnetic fields of the kind produced by power lines was found.

a. Was this an observational study or an experiment? Justify your answer.

b. Does this study prove that living near power lines doesn鈥檛 cause cancer? Explain your answer.

The Large Counts condition When constructing a confidence interval for a population proportion, we check that both np鈭�andn1-p鈭�are at least 10

a. Why is it necessary to check this condition?

b. What happens to the capture rate if this condition is violated?

Explaining confidence A 95%confidence interval for the mean body mass index (BMI) of young American women is 26.8卤0.6. Discuss whether each of the following explanations is correct, based on that information.

a. We are confident that 95%of all young women have BMI between 26.2and 27.4.

b. We are 95%confident that future samples of young women will have mean BMI

between 26.2and27.4.

c. Any value from 26.2to27.4is believable as the true mean BMI of young American women.

d. If we take many samples, the population mean BMI will be between 26.2and 27.4in about 95%of those samples.

e. The mean BMI of young American women cannot be 28.
See all solutions

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