For all the questions consider µ1 and µ2 are population means, 12 and 22 are the population variances, are the sample means

Note:For all the questions consider µ₁ and µ₂ are population means, ₁² and ₂² are the population variances, are the sample means , S₁² and S₂² are the sample variances,n₁ and n₂ are the sample sizes  of group 1 and group 2 respectively.

10.9 A problem with a telephone line that prevents a customer from receiving or making calls is disconcerting to both the customer and the telephone company. The data in the file PHONE represent samples of 20 problems reportedto two different offices of a telephone company and the timeto clear these problems (in minutes) from the customers lines:

Central Office I Time to Clear Problems (minutes)

1.48 1.75 0.78 2.85 0.52 1.60 4.15 3.97 1.48 3.10

1.02 0.53 0.93 1.60 0.80 1.05 6.32 3.93 5.45 0.97

Central Office II Time to Clear Problems (minutes)

7.55 3.75 0.10 1.10 0.60 0.52 3.30 2.10 0.58 4.02

3.75 0.65 1.92 0.60 1.53 4.23 0.08 1.48 1.65 0.72

a. Assuming that the population variances from both offices are equal, is there evidence of a difference in the mean waiting time between the two offices? (Use α=0.05 .)

b. Find the p-value in (a) and interpret its meaning.

c. What other assumption is necessary in (a)?

10.11 Digital cameras have taken over the majority of the point-and-shoot camera market. One of the important features of a camera is the battery life as measured by the number of shots taken until the battery needs to be recharged. The data in the file Digitalcameras contain the battery life of 31 subcompact cameras and 15 compact cameras (data extracted from “Cameras,” Consumer Reports, November 2006, pp. 20-21).

a. Assuming that the population variances from both types of digital cameras are equal, is there evidence of a difference in the mean battery life between the two types of digital cameras (α= 0.05)?

b. Determine the p-value in (a) and interpret its meaning.

10.21 In industrial settings, alternative methods often exist for measuring variables of interest. The data in the file Measurement (coded to maintain confidentiality) represent measurements in-line that were collected from an analyzer during the production process and from an analytical lab (extracted from M. Leitnaker, “ComparingMeasurement Processes: In-line Versus AnalyticalMeasurements,” Quality Engineering, 13, 2000 2001, pp.293–298).

a. At the 0.05 level of significance, is there evidence of adifference in the mean measurements in-line and from ananalytical lab?

b. What assumption is necessary about the population distribution in order to perform this test?

10.23 A newspaper article discussed the opening of a Whole Foods Market in the Time-Warner building in New York City. The following data (stored in the file Wholefood 1 ) comparedthe prices of some kitchen staples at the new Whole Foods Market and at the Fairway supermarket located about 15 blocks from the Time-Warner building: Source: Data extracted from W. Grimes, “A Pleasure Palace Without the Guilt,” The New York Times, February 18, 2004, pp. F1, F5.

a. At the 0.01 level of significance, is there evidence that the mean price is higher at Whole Foods Market than at the Fairway supermarket?

b. Interpret the meaning of the p-value in (a).

c. What assumption is necessary about the population distribution in order to perform the test in (a)?

10.49 The director of training for a company that manufactures electronic equipment is interested in determining whether different training methods have an effect on the productivity of assembly-line employees. She randomly assigns 21 of the 42 recently hired employees to a computer-assisted, individual-based training program. The other 21

are assigned to a team-based training program. Upon completion of the training, the employees are evaluated on the time (in seconds) it takes to assemble a part. The results are in the data file  Training.

a. Using a 0.05 level of significance, is there evidence of a difference between the variances in assembly times (in seconds) of employees trained in a computer-assisted, individual-based program and those trained in a team based program?

b. On the basis of the results in (a), which t test defined in Section 10.1 should you use to compare the means of the two training programs? Discuss.