# Hypothesis Testing With Single Samples

1. 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?

2. Do students at your school study more, less, or about the same as at other business schools? Business Week

reported that at the top 50 business schools, students studied an average of 14.6 hours (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

benchmark 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?

3. 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 the specified value of 375 hours. State the null and alternative hypotheses.

4. 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.

5. The Glen Valley Steel Company manufactures steel bars. If the production process is working properly, it turns out steel bars that are normally distributed with mean length of at least 2.8 feet. Longer steel bars can be used or altered, but shorter bars must be scrapped. You select a sample of 25 bars, and the mean length is 2.73 feet and the sample standard deviation is 0.20 foot. Do you need 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 value approach 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-value

approach to hypothesis testing?

c. Interpret the meaning of the p-value in this problem.

d. Compare your conclusions in (a) and (b).

6. Late payment of medical claims can add to the cost of health care. An article (M. Freudenheim, "The Check Is Not in the Mail," The New York Times, May 25, 2006, pp. C1, C6) reported that for one insurance company, 85.1% of the claims were paid in full when first submitted. Suppose that the insurance company developed a new payment system in an effort to increase this percentage. A sample of 200 claims processed under this system revealed that 180 of the claims were 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 this new system is higher than the article reported for the previous system?

b. Compute the p-value and interpret its meaning.

#### Solution Summary

Hypothesis testing with single samples are examined.