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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

Losing weight A Gallup poll asked a random sample of U.S. adults, 鈥淲ould you like to lose weight?鈥� Based on this poll, the 95%confidence interval for the population

proportion who want to lose weight is (0.56,0.62).

a. Interpret the confidence interval.

b. What is the point estimate that was used to create the interval? What is the margin of error?

c. Based on this poll, Gallup claims that more than half of U.S. adults want to lose weight. Use the confidence interval to evaluate this claim.

How confident? The figure shows the result of taking 25SRSs from a Normal population and constructing a confidence interval for the population mean using each sample. Which confidence level鈥攔ole="math" localid="1654197644211" 80%,90%,95%,or99%鈥攄o you think was used? Explain your reasoning.

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 95% confidence interval based on n=10 randomly selected observations

b. A99% confidence interval from an SRS of 20 observations

c. A 90% confidence interval based on a random sample of 77 individuals

More Oranges:The gardener in the previous exercise randomly selects 20

mandarin oranges from the tree and counts the number of seeds in each orange. Here are the data:

a. Graph the data using a dot plot.

b. Based on your graph, is it plausible that the number of seeds from oranges on this tree follows a distribution that is approximately Normal? Explain your answer.

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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