# Confidence interval for mean and ANOVA

1. An experiment was performed to compare the abrasive wear of two different laminated materials. Twelve pieces of material 1 were tested, by exposing each piece to a machine measuring wear. Ten pieces of material 2 were similarly tested. In each case, the depth of wear was observed. The samples of the material 1 gave an average of 85 units with a sample standard deviation of 4, while the samples of material 2 gave an average of 81 units and a sample deviation of 5. Can you conclude at the 0.05 level of significance that the abrasive wear of material 1 exceeds that of material 2 by more than 2 units? Assume the populations to be approximately normal with equal variances.

a. State the hypothesis:

b. State the value of the proper test statistic to the nearest hundredth:

c. State the decision rule using the proper critical value:

d. State the conclusion using the decision rule from part (c):

e. Is the assumption of equal population variances a valid assumption? (Show all work in a logically structured manner).

2. The manufacturing company in problem produces electric insulators. If the insulators break when in use, a short circuit is likely to occur. To test the strength of the insulators, destructive testing in high-powered labs is carried out to determine how much force is required to break the insulators. Force is measured by observing how many pounds must be applied to the insulator before it breaks. Data are collected from a sample of 30 insulators. At the 0.05 level of significance, is there evidence that the population mean force is greater than 1700 pounds? The file force contains the strengths as follows:

1,870 1,728 1,656 1,610 1,634 1,784 1,522 1,696

1,592 1,662 1,866 1,764 1,734 1,662 1,734 1,774

1,550 1,756 1,762 1,866 1,820 1,744 1,788 1,688

1,810 1,752 1,680 1,810 1,652 1,736

a). State the Hypothesis:

b). State the value of the proper test statistic to the nearest hundredth:

c). State the decision rule using the proper critical value:

d). State the conclusion using the decision rule from part (c)

e). What is the p-value for the test? What is your conclusion of he test based on the p-value?

3. A certain change in a manufacturing procedure for component parts is being considered. Samples are taken using both the existing and the new procedure in order to determine if the new procedure results in an improvement.

a. If 75 of 1500 items from the existing procedure were found to be defective and 80 of 2000 items from the new procedure were found to be defective, find the 90% confidence interval for the true difference in the fraction of defectives between the existing and the new process.

b. Based on the confidence interval in part (a), what is your conclusion regarding whether or not there is a statistically significant difference between the existing procedure and the new procedure?

4. A hospital conducted a study of the waiting time in its emergency room. The hospital has a main campus and three satellite locations. Management had a business objective of reducing waiting time for emergency room cases that did not require immediate attention. To study this, a random sample of 15 emergency room cases that did not require immediate attention in each location were selected on a particular day, and the waiting time measured from the check-in to when the patient was called into the clinic area was measured. At the 0.05level of significance, is there evidence of a difference in the mean waiting times in the four locations? Below is the data for this study:

Main Satellite1 Satellite2 Satellite3

120.08 30.75 75.86 54.05

81.90 61.83 37.88 38.82

78.79 26.40 68.73 36.85

63.83 53.84 51.08 32.83

79.77 72.30 50.21 52.94

47.94 53.09 58.47 34.13

79.88 27.67 86.29 69.37

48.63 52.46 62.90 78.52

55.43 10.64 44.84 55.95

64.06 53.50 64.17 49.61

64.99 37.28 50.68 66.40

53.82 34.31 47.97 76.06

62.43 66.00 60.57 11.37

65.07 8.99 58.37 83.51

81.02 29.75 30.40 39.17

a. State the hypothesis:

b. State the value of the proper test statistic to the nearest hundredth:

c. State the decision rule using the critical value:

d. State the conclusion using the decision rule from part (c):

e. If appropriate, determine which locations differ in mean waiting time

f. One of the assumptions for ANOVA is the homogeneity of variance. At the 0.05 level of significance, is there evidence of a difference in the variation in waiting time among the four locations? This question should be answered simply using the p-value for the appropriate test.

#### Solution Summary

Step by step method for computing test statistic for One way ANOVA and confidence interval is given in the answer.