1. Suppose the mean pulse rate of college students is 68 beats per minute with a standard deviation of 12.5. You conduct a special exercise program for 31 college students. After completing the program, the mean pulse rate of the students was 63.1. Test the hypothesis that the program lowered students’ pulse rates using a = 0.01.
2. A car company claims that its compact model gets 33 miles per gallon. A government inspector tests 12 of the company cars and finds that the average mileage is 29.9 mpg with a standard deviation of 1.2 mpg. Test if the mileage found is significantly less than the mileage claimed by the company using a = 0.01.
3. A magazine claims that its readers have an average annual income of $43,725 with a standard deviation of $3,456. You randomly sample on 27 of the magazine’s readers and an average income of $38,251. Determine if the income of the readers is significantly less than the income claimed by the company using a = 0.01 and the prob-value approach.
Confidence Intervals
1. A U.S. labor economist interviews 900 workers and finds that the mean number of hours they worked in the last week was 38.9 with a standard deviation of 3.6 hours. Make a 99% confidence interval for the mean of all workers in the U.S.
2. An auto parts company is interested in how long people plan to own their cars. They collect the following data by asking 18 car owners how many years they will drive their current car from the time they bought it until they trade it in:
5 7 8 4 9 10 8 5 4 1 1 2 4 3 5 4 2 7
Make a 95% confidence interval for the length of time these car owners will keep their cars.
3. A researcher studying salaries of police officers around the nation surveyed 64 officers and found a mean salary of $71,228 with a standard deviation of $7,425. Make a 99% confidence interval for the mean salary of all police officers.
