Q1. If you use a 0.10 level of significance in a (two-tail) hypothesis test, what is your decision rule for rejecting a null hypothesis that the population mean is 500 if you use the Z test?
Q2. Do students at your school study more, less, or about the same as at other business schools? Business Weekreported that at the top 50 business schools, students studiedan average of 14.6 hours (data extracted from"Cracking the Books," SPECIAL REPORT/Online Extra, www.businessweek.com, March 19, 2007). Set up ahypothesis test to try to prove that the mean number ofhours studied at your school is different from the 14.6 hourbenchmark reported by Business Week.
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?
Q3. The quality control manager at a lightbulb factory needs to determine whether the mean life of a large shipmentof lightbulbs is equal to the specified value of 375hours. State the null and alternative hypotheses.
Q4. 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 8ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidencethat the mean amount packaged is different from 8.17ounces. 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 differentfrom 8.17 ounces? (Use a 0.05 level of significance.)
b. Determine the p-value and interpret its meaning.
Q5. The Glen Valley Steel Company manufactures steel bars. If the production process is workingproperly, it turns out steel bars that are normally distributedwith mean length of at least 2.8 feet. Longer steel barscan be used or altered, but shorter bars must be scrapped.You select a sample of 25 bars, and the mean length is 2.73feet and the sample standard deviation is 0.20 foot. Do youneed to adjust the production equipment?
a. If you test the null hypothesis at the 0.05 level of significance, what decision do you make using the critical valueapproach to hypothesis testing?
b. If you test the null hypothesis at the 0.05 level of significance, what decision do you make using the p-valueapproach to hypothesis testing?
c. Interpret the meaning of the p-value in this problem.
d. Compare your conclusions in (a) and (b).
Q6. Late payment of medical claims can add to the cost of health care. An article (M. Freudenheim, "The Check Is Notin the Mail," The New York Times, May 25, 2006, pp. C1,C6) reported that for one insurance company, 85.1% of theclaims were paid in full when first submitted. Suppose thatthe insurance company developed a new payment system inan effort to increase this percentage. A sample of 200 claimsprocessed under this system revealed that 180 of the claimswere paid in full when first submitted.
a. At the 0.05 level of significance, is there evidence that the population proportion of claims processed under thisnew system is higher than the article reported for the previoussystem?
b. Compute the p-value and interpret its meaning.