1. Do students at your school study more than, less than, or about the same as students at other business schools? BusinessWeek reported that at the top 50 business schools, students studied an average of 14.6 hours per week. (Data extracted from "Cracking the Books," Special Report/Online Extra, www.businessweek.com, March 19, 2007.) Set up a hypothesis test to try to prove that the mean number of hours studied at your school is different from the 14.6-hour-per-week benchmark reported by BusinessWeek.
a. State the null and alternative hypotheses.
b. What is a Type I error for your test?
c. What is a Type II error for your test?
2. The quality-control manager at a light bulb factory needs to determine whether the mean life of a large shipment of light bulbs is equal to 375 hours. The population standard deviation is 100 hours. A random sample of 64 light bulbs indicates a sample mean life of 350 hours.
a. At the 0.05 level of significance, is there evidence that the mean life is different from 375 hours?
b. Compute the p-value and interpret its meaning.
c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs.
d. Compare the results of (a) and (c). What conclusions do you reach?
3. A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces. Suppose that in a particular sample of 50 packages, the mean amount dispensed is 8.159 ounces, with a sample standard deviation of 0.051 ounce.
a. Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 0.05 level of significance.)
b. Determine the p-value and interpret its meaning.
4. Southside Hospital in Bay Shore, New York, commonly conducts stress tests to study the heart muscle after a person has a heart attack. Members of the diagnostic imaging department conducted a quality improvement project with the objective of reducing the turnaround time for stress tests. Turnaround time is defined as the time from when a test is ordered to when the radiologist signs off on the test results. Initially, the mean turnaround time for a stress test was 68 hours. After incorporating changes into the stress-test process, the quality improvement team collected a sample of 50 turnaround times. In this sample, the mean turnaround time was 32 hours, with a standard deviation of 9 hours.
a. If you test the null hypothesis at the 0.01 level of significance, is there evidence that the new process has reduced turnaround time?
b. Interpret the meaning of the p-value in this problem.
5. The U.S. Department of Education reports that 46% of full-time college students are employed while attending college. (Data extracted from "The Condition of Education 2009," NationalCenter for Education Statistics, nces.ed. gov.) A recent survey of 60 full-time students at MiamiUniversity found that 29 were employed.
a. Use the five-step p-value approach to hypothesis testing and a 0.05 level of significance to determine whether the proportion of full-time students at MiamiUniversity is different from the national norm of 0.46.
b. Assume that the study found that 36 of the 60 full-time students were employed and repeat (a). Are the conclusions the same?