Estimating the Difference between Two Population Proportions — Unit test Answers

What is the z* critical value for constructing a 95% confidence interval for a proportion?Find the z-table here.

A political candidate feels that she performed particularly well in the most recent debate against her opponent. Her campaign manager polled a random sample of 400 likely voters before the debate and a random sample of 500 likely voters after the debate. The 95% confidence interval for the true difference (post-debate minus pre-debate) in proportions of likely voters who would vote for this candidate was (–0.014, 0.064). What was the difference (pre-debate minus post-debate) in the sample proportions of likely voters who said they will vote for this candidate?

After a hailstorm, a large car dealership wants to determine the proportion of cars that have damage. The service department randomly selects 50 cars on the dealership lot, examines them, and finds that 11 cars have damage. They want to construct a 99% confidence interval for the true proportion of cars with damage from the storm. Are the conditions for inference met?

A random sample of high school seniors was surveyed about whether they drive to school. Of the 75 seniors surveyed, 64 stated they drive to school. Which of the following is the 90% confidence interval for p, the proportion of all high school seniors who drive to school?Find the z-table here.

The school board of a large school district would like to raise taxes in the district to pay for new computers. To see if there is support for a tax increase, they send a survey home with a random sample of students in the district. If the survey is not completed, calls are made to ensure responses are obtained from the parents of every selected student. The survey asks, "Would you be in favor of a modest tax increase to fund the purchase of new computers for all students?” The confidence interval for the true proportion of families that are in favor of a tax increase is 0.70 to 0.80. Members of the community who do not have children in the district complain about not being included in this study. Which of the following sources of bias affected the confidence interval, but is not included among the sources covered by the margin of error?

A major car dealership has several stores in a big city. The owner wants to determine if there is a difference in the proportions of SUVs that are sold at stores A and B. The owner gathers the sales records for each store from the past year. A random sample of 55 receipts from store A shows that 30 of the sales were for SUVs. Another random sample of 60 receipts from store B shows that 45 of the sales were for SUVs.Based on the 99% confidence interval, (–0.43, –0.02), is there convincing evidence of a difference in the proportions of sales that are SUVs for the two stores?

A school nurse would like to estimate the true mean amount of sleep that students at the high school get per night. To do so, she selects a random sample of 30 students and determines that the 90% confidence interval for the true mean number of hours of sleep that high school students get per night to be 6.5 to 7.5 hours. Which of these statements is a correct interpretation of the confidence level?

A political candidate feels that she performed particularly well in the most recent debate against her opponent. Her campaign manager polled a random sample of 400 likely voters before the debate and a random sample of 500 likely voters after the debate. The 95% confidence interval for the true difference (post-debate minus pre-debate) in proportions of likely voters who would vote for this candidate was (–0.014, 0.064). Based on this interval, what conclusion should the candidate make about the proportion of likely voters who would vote for her in the upcoming election?

Nick selects a simple random sample of 25 seniors at his large school and finds that 20 of them eat a healthy breakfast. He wants to construct a confidence interval for p = the proportion of all seniors at this school who eat a healthy breakfast, but he realizes he hasn’t met all the conditions for constructing the interval. Which condition for this procedure has he failed to meet?

A statistics student wants to survey a high school of 910 students concerning support for increasing the number of student parking spots. The student randomly selects 100 students to construct a 95% confidence interval for the true proportion of students who support increasing the number of student parking spots, and finds that 77 students are in support. Are the conditions for inference met?

A school nurse would like to estimate the true mean amount of sleep that students at the high school get per night. To do so, she selects a random sample of 30 students and determines that the 90% confidence interval for the true mean amount of sleep that high school students get per night to be 6.5 to 7.5 hours. Which of the following would decrease the width of the interval?

The cafeteria manager at a high school that has 910 students and 75 teachers is considering adding a baked potato bar to the lunch menu. The manager randomly surveys 90 students and 25 teachers, and finds that 50 of the 90 students and 13 of the 25 teachers would purchase from the potato bar. The manager constructs a 99% confidence interval for the difference in the proportions of students and teachers who would purchase lunch on the day the potato bar option is available. Are the conditions for inference met?

Twenty-four pairs of adult brothers and sisters were sampled at random from a population. The difference in heights, recorded in inches (brother’s height minus sister’s height), was calculated for each pair. The 95% confidence interval for the mean difference in heights for all brother-and-sister pairs in this population was (–0.76, 4.34). What is the margin of error for the confidence interval?

A statistics class weighed 20 bags of grapes purchased from the store. The bags are advertised to contain 16 ounces, on average. The class calculated the 90% confidence interval for the true mean weight of bags of grapes from this store to be (15.875, 16.595) ounces. What is the correct interpretation of the 90 percent confidence interval?

The owner of a popular coffee shop wants to determine if there is a difference between the proportion of customers who use their own cups when they purchase a coffee beverage, and the proportion of customers who use their own cups when they purchase an espresso beverage. Customers using their own cups get a 5% discount, which is displayed on the receipt. The owner randomly selects 50 receipts from all coffee purchases and 50 receipts from all espresso purchases. For coffee purchases, 24 receipts showed that the customer used their own cup. For espresso purchases, 18 receipts showed that the customer used their own cup. Assuming the conditions for inference have been met, what is the 99% confidence interval for the difference in proportion of customers who use their own cups?Find the z-table here.