Estimating the Difference between Two Population Proportions — Unit test Answers

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?

A teacher would like to estimate the mean number of steps students take during the school day. To do so, she selects a random sample of 50 students and gives each one a pedometer at the beginning of the school day. They wear the pedometers all day and then return them to her at the end of the school day. From this, she computes the 98% confidence interval for the true mean number of steps students take during the school day to be 8,500 to 10,200 steps. Which of these statements is a correct interpretation of the confidence level?

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?

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.

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?

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.

A therapist wanted to determine if yoga or meditation is better for relieving stress. The therapist recruited 100 of her high-stress patients. Fifty of them were randomly assigned to take weekly yoga classes, and the other 50 were assigned weekly meditation classes. After one month, 30 of the 50 patients in the yoga group reported less stress, and 35 of the 50 patients in the meditation group reported less stress. Assuming the conditions for inference are met, what is the 95% confidence interval for the difference in proportions of patients experiencing stress relief from the yoga and meditation groups?Find the z-table here.

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?

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

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 95% confidence interval for the true proportion of math students who prefer to use a handheld calculator versus computer software for computations is (0.751, 0.863). Is it reasonable to believe more than 75% of math students prefer to use a handheld calculator versus computer software for computations?

The manager of a large manufacturing company wants to estimate the proportion of items that have been manufactured with defects. How many items are required for a random sample to obtain a margin of error of at most 0.04 with 90% confidence?Find the z-table here.

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?

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?

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?