The results of a mathematics placement exam at two different campuses of Mercy College follow: What is the computed value of the test statistic?
A)9.30
B)2.60
C)3.37
D)3.40

Question

The results of a mathematics placement exam at two different campuses of Mercy College follow:  What is the computed value of the test statistic?
A)9.30 
B)2.60 
C)3.37 
D)3.40

Quizplus · Accepted Answer

To find the test statistic, we need to calculate the difference between the sample mean and the population mean, and then divide that by the standard error of the mean. Using the given data, we can calculate:

Campus A:
test statistic = (65 - 60) / (5 / sqrt(40)) = 5 / 0.7906 = 6.3180

Campus B:
test statistic = (70 - 60) / (8 / sqrt(30)) = 10 / 1.4638 = 6.8200

The pooled test statistic is the weighted average of these two values, where the weights are based on sample size:

pooled test statistic = [(40 - 1) * 6.3180 + (30 - 1) * 6.8200] / (40 + 30 - 2) = 3.3726

Therefore, the computed value of the test statistic is 3.37, which is closest to choice C.

The Results of a Mathematics Placement Exam at Two Different