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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

America鈥檚 favorite cookie Ann and Tori wanted to estimate the average weight of an Oreo cookie to determine if it was less than advertised (34 grams for 3 cookies). They selected a random sample of 36cookies and found the weight of each cookie (in grams). The mean weight was x虅=11.3921grams with a standard deviation of sX=0.0817grams. Construct and interpret a 90%confidence interval for the true mean weight of an Oreo cookie.

Teens and their TV sets According to a Gallup Poll report, 64%of teens aged 13to 17have TVs in their rooms. Here is part of the footnote to this report:

These results are based on telephone interviews with a randomly selected national sample of 1028teenagers in the Gallup Poll Panel of households, aged 13to 17. For results based on this sample, one can say that the maximum error attributable to sampling and other random effects is 卤3percentage points. In addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of public opinion polls.

a. We omitted the confidence level from the footnote. Use what you have learned to estimate the confidence level, assuming that Gallup took an SRS.

b. Give an example of a 鈥減ractical difficulty鈥� that could lead to bias in this survey.

The U.S. Forest Service is considering additional restrictions on the number of vehicles allowed to enter Yellowstone National Park. To assess public reaction, the service asks a random sample of 150 visitors if they favor the proposal, Of these, 89 say "Yes."

a. Construct and interpret a 99%confidence interval for the proportion of all visitors to Yellowstone who favor the restrictions.

b. Based on your work in part (a), is there convincing evidence that more than half of all visitors to Yellowstone National Park favor the proposal? Justify your answer.

Critical values What critical value t*from Table B should be used for a confidence interval for the population mean in each of the following situations?

a. A 90% confidence interval based on n=12 randomly selected observations

b. A 95% confidence interval from an SRS of 30 observations

c. A 99% confidence interval based on a random sample of size 58

The Gallup Poll interviews 1600 people. Of these, 18% say that they jog regularly. The news report adds: 鈥淭he poll had a margin of error of plus or minus three percentage points at a 95% confidence level.鈥� You can safely conclude that

a. 95% of all Gallup Poll samples like this one give answers within 卤3% of the true population value.

b. the percent of the population who jog is certain to be between 15% and 21%.

c. 95% of the population jog between 15% and 21% of the time.

d. we can be 95% confident that the sample proportion is captured by the confidence interval.

e. if Gallup took many samples, 95% of them would find that 18% of the people in the sample jog.
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