The following data are scores on a standardized statistics examination for indep

Question

The following data are scores on a standardized statistics examination for independent random samples of students from two small liberal arts colleges. College A: 78. 84. 81. 78, 76, 83. 79. 75, 85. 81 College B: 88. 77. 81. 85. 83. 76. 89. 93. 88. 84 Use these data for questions on this task. Consider the test of hypothesis Ho: Populations have the same location parameter. Ha: Populations have different location parameters. Calculate the test statistic T for the Wilcox on rank sum test. For alpha = 0.05. use Table 5 to specify the rejection region. Use information in Questions 1 and 2 to make a decision about Ho. Calculate the approximate z test statistic for the Wilcox on rank sum test. Use the approximate test statistic from Question 4 to calculate the P-value. For alpha = 0.05. use information in Questions 4 and 5 to make a decision about Ho.

Explanation / Answer

Solution :

Here W+ is sum of positive ranks and W+ is sum of positive numbers

I]Test statistics T=minimum(W+,W-)

II]The critical value for this test with n=10 and =0.05 is Tcrit=8 and

III] decision rule: Reject H0 if T < 8.

3. As T>8 ,we fail to reject null hypothesis hence we conclude that population have the same location parameter

Collage B X-Y |X-Y| rank 88 -10 10 2.5 77 7 7 5.5 81 0 0 10 85 -7 7 5.5 83 -7 7 5.5 76 7 7 5.5 89 -10 10 2.5 93 -18 18 1 88 -3 3 8.5 84 -3 3 8.5 W+ 11 W- 44 statistics 11

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