AP Stats Chapter 8 Practice Test

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

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

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

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

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

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

Answer explanation

95% of confidence intervals will capture the true proportion, not any particular sample proportion.

A confidence interval for a difference in proportions is −0.077 to 0.013. What are the point estimate rounded to 3 decimal places.

Answer explanation

The point estimate is the midpoint of the interval.

A confidence interval for a difference in proportions is −0.077 to 0.013. What is the margin of error rounded to 3 decimal places.

Answer explanation

The margin of error is the distance from the point estimate to the endpoints of the interval.

In a random sample of 100 students from a large high school, 37 regularly bring a reusable water bottle from home. Which of the following gives the correct value and interpretation of the standard error of the sample proportion?

• In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home will be at most 0.048 from the true proportion.

• In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.095 from the true proportion.

• In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion.

• There is not enough information to calculate the standard error.

• In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home will be at most 0.095 from the true proportion.

Answer explanation

Because 𝑛 = 100 < 10% of all students at this large high school the standard error of 𝑝̂ is approximately √(0.37(1−0.37)/100) = 0.048.

Many television viewers express doubts about the validity of certain commercials. In an attempt to answer their critics, Timex Group USA wishes to estimate the true proportion p of all consumers who believe what is shown in Timex television commercials. What is the smallest number of consumers that Timex can survey to guarantee a margin of error of 0.05 or less at a 99% confidence level?

• 550

• 600

• 650

• 700

• 750

What is the critical value for calculating a 94% confidence interval for a population proportion?

Enter the critical value to 2 decimal places.

Answer explanation

In a 94% confidence interval, the tail area is (1 – 0.94)/2 = 0.03. Use invNorm or a standard normal table to determine the critical value for this tail area.

A radio talk show host with a large audience is interested in the proportion 𝑝� of adults in his listening area who think the drinking age should be lowered to eighteen. To find this out, he poses the following question to his listeners: “Do you think that the drinking age should be reduced to eighteen in light of the fact that 18-year-olds are eligible for military service?” He asks listeners to go to his website and vote “Yes” if they agree the drinking age should be lowered and “No” if not. Of the 100 people who voted, 70 answered “Yes.” Which of the following conditions are violated?

• Random

• 10%

• Large Counts

• Random, 10%, Large Counts

• Random, 10%

Answer explanation

This is a voluntary response sample, so it is not random.

A marketing assistant for a technology firm plans to randomly select 1000 customers to estimate the proportion who are satisfied with the firm’s performance. Based on the results of the survey, the assistant will construct a 95% confidence interval for the proportion of all customers who are satisfied. The marketing manager, however, says that the firm can afford to survey only 250 customers. How will this decrease in sample size affect the margin of error and confidence interval? MARK ALL THAT APPLY.

• The Margin of Error will be twice as large

• The Margin of Error will be four times as large

• The Margin of Error will be half as large

• The confidence interval will be wider

• The confidence interval will be narrower

Answer explanation

Because the sample size of 250 is 1/4 of the sample size of 1000, the margin of error will be about 2 times as large.

Thirty-five people from a random sample of 125 workers from Company A admitted to using sick leave when they weren’t really ill. Seventeen employees from a random sample of 68 workers from Company B admitted that they had used sick leave when they weren’t ill. Which of the following is a 95% confidence interval for the difference in the proportions of workers at the two companies who would admit to using sick leave when they weren’t ill?

Answer explanation

Formula for a confidence interval for the difference in two proportions is:

A telephone poll of an SRS of 1234 adults found that 62% are generally satisfied with their lives. The announced margin of error for the poll was 3%. Does the margin of error account for the fact that some adults do not have telephones?

• Yes; taking an SRS eliminates any possible bias in estimating the population proportion.

• No; the margin of error only accounts for sampling variability.

• Yes; the margin of error accounts for undercoverage but not nonresponse.

• No; the margin of error accounts for nonresponse but not undercoverage.

• Yes; the margin of error accounts for all sources of error in the poll.

Answer explanation

An SRS eliminates bias in the choice process but does not help with bias like undercoverage. The margin of error does not account for any bias that is part of the data collection process.