Cumulative Exam — Cumulative exam Answers

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. The therapist wants to construct a 95% confidence interval for the difference in proportions of patients experiencing stress relief after yoga and after meditation. Are the conditions for inference met?

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 90 students, and finds that 63 support increasing the number of student parking spots. Assuming the conditions for inference have been met, what is the 95% confidence interval for the true proportion of students who would support the increase in the number of parking spots?

A math teacher is investigating the problem of students losing their graphing calculators because their names aren’t written on them. In a random sample of 50 students, only 32 had their names written on their graphing calculators. The teacher constructs a 99% confidence interval for the proportion of all students at this school who have their names written on their graphing calculators and obtains (0.465, 0.815). What is the correct interpretation of this confidence interval?

A laundry detergent company wants to determine if a new formula of detergent, A, cleans better than the original formula, B. Researchers randomly assign 500 pieces of similarly soiled clothes to the two detergents, putting 250 pieces in each group. After washing the clothes, independent reviewers determine the cleanliness of the clothes on a scale of 1–10, with 10 being the cleanest. The researchers calculate the proportion of clothes in each group that receive a rating of 7 or higher. For detergent A, 228 pieces of clothing received a 7 or higher. For detergent B, 210 pieces of clothing received a rating of 7 or higher. Assuming the conditions for inference are met, what is the 90% confidence interval for the difference in proportions of clothes that receive a rating of 7 or higher for the two detergents?Find the z-table here.

A clinic measured the systolic blood pressure for a random sample of 10 patients. The resulting 95% confidence interval for the mean systolic blood pressure of all the patients at this clinic was (111.3, 129.5). What was the margin of error for this confidence interval?

The proportion of customers who pay their credit card bill on time is 84%. Administrators at a large university believe less than 84% of the students enrolled pay their credit card bill on time. The 95% confidence interval for the true proportion of students enrolled in this university who pay their credit card bill on time is (0.791, 0.839). Is it reasonable to believe the true proportion of students at this university who pay their credit card bill on time is less than 84%?

In a small town of 5,832 people, the mayor wants to determine the proportion of voters who would support an increase to the food tax. An assistant to the mayor decides to survey 1,000 randomly chosen people to construct a 90% confidence interval for the true proportion of people who would support the increase in food tax. Of the sample, 363 people say they would support the increase. Are the conditions for inference met?

A computer company wants to determine if there is a difference in the proportion of defective computer chips in a day’s production from two different production plants, A and B. A quality control specialist takes a random sample of 100 chips from the first hour of production from plant A and determines that there are 12 defective chips. The specialist then takes a random sample of 100 chips from the last hour of production from plant B and determines that there are 10 defective chips. Assuming conditions for inference are met, what is the 90% confidence interval for the true difference in proportions of defective chips from a day’s production between the two plants? Find the z-table here.

A clinic measured the systolic blood pressure for a random sample of 10 patients. The resulting 95% confidence interval for the mean systolic blood pressure of all the patients at this clinic was (111.3, 129.5). A doctor commented that, on average, the patients at this clinic have high blood pressure, which is defined as blood pressure over 130. Based on the confidence interval, is the doctor’s statement justified?

A clinic measured the systolic blood pressure for a random sample of 10 patients. The resulting 95% confidence interval for the mean systolic blood pressure of all the patients at this clinic was (111.3, 129.5). What was the mean systolic blood pressure from the sample of 10 patients?