1. The American Management Association surveys middle managers in the retail industry and wants to estimate their mean annual income. A random sample of 36 managers reveals a sample mean of $51,390. The standard deviation of this population is $1,030. Use a 95% confidence interval for this problem.
a. What is the best point estimate of the population mean?
b. What is a reasonable range of values for the population mean, i.e. upper and lower end of the confidence interval?
c. What do these results mean?
2. Jamestown Steel Company manufactures and assembles desks and other office equipment. The weekly production of the Model A325 desk at the Fredonia Plant follows the normal probability distribution with a mean of 195 and the standard deviation in the population is unknown. Recently, new production methods have been introduced and new employees hired. The VP of manufacturing would like to investigate whether there has been a change in the weekly production of the Model A325 desk. Use the .01 level of statistical significance. The sample size is 64 and the sample mean is 209.4. The sample standard deviation is 12. Show all work and your answer must include all 6 steps in the hypothesis test.
For questions 3, 4, and 5 rely on the following table:
|
Sample
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
|
1
|
56
|
47
|
47
|
48
|
58
|
55
|
62
|
|
2
|
55
|
51
|
52
|
40
|
53
|
47
|
54
|
|
3
|
42
|
46
|
48
|
46
|
41
|
50
|
52
|
|
4
|
52
|
49
|
55
|
47
|
49
|
46
|
56
|
3. Use samples 2 and 3. Assume the population standard deviations are unknown, but equal. Assume both populations follow normal distributions; the two samples are unrelated and independent. Relying on the two-sample t test of means, 3 assuming equal standard deviations, we want to test a hypothesis that the mean for sample 2 is greater than the mean for sample 3. We want the .05 level of significance. State the null hypothesis and alternative hypothesis. State the alpha level, select the test statistic. Formulate the decision rule, make a decision, and interpret the results.
4. Use samples 2 and 3. Assume the population standard deviations are unknown, and unequal. Assume both populations follow normal distributions, the two samples are unrelated and independent. Perform the two-sample t test of means, assuming unequal standard deviations. We want to test a hypothesis that the mean for sample 3 is greater than the mean for sample 2. We want the .01 level of significance. State the null hypothesis and alternative hypothesis. State the alpha level, select the test statistic. Formulate the decision rule, make a decision, and interpret the results.
5. Use samples 1 and 4. Assume both populations follow normal distributions, the two samples are related and dependent. We are not given information about the population standard deviations. Perform the two-sample t test with matching/paired/dependent samples. We want to test a hypothesis that there is a difference in the measurements of the two samples. We want the .05 level of significance. State the null hypothesis and alternative hypothesis. State the alpha level, select the test statistic. Formulate the decision rule, make a decision, and interpret the results.