The sample data below were artificially generated by sampling with the Excel random number generator in normal distribution mode. Variable X1 was deliberately made to have a much larger population variance than variable X2, whereas in virtually all of the textbook examples and problems, the assumption of equal population variances is made (“pooled variance”).

Test whether the population mean of X1 larger than that of X2. When you compute the sample means you will see that the sample mean for X1 is a little larger than for X2, but is this significant at the 0.05 level? What is its level of significance (p-value)?

Use the Excel tool for unequal variance.

81.89291652 68.32479

66.30485945 59.64873

58.55150807 61.55066

79.38375706 58.91033

69.94111022 55.63936

85.53003131 64.79779

99.00587788 60.14308

64.89543825 53.81751

44.01473593 59.75551

59.8413

66.57747

63.9125

a) Decision is:

b) Test t =

c) p-value for this test is =

d) Critical t value(s) is/are

Problem 10

Repeat problem 9 with the Excel tool for equal (“pooled”) variance to see how different its answers are.

Of course, answers for the pooled method are suspect in this case.

a) Decision is:

b) Test t =

c) p-value for this test is =

d) Critical t value(s) is/are