The results of a mathematics placement exam at two different campuses of Mercy College follow: Given that the two population standard deviations are known,what is the p-value?
A)1.0
B)0.0
C)0.05
D)0.95

Question

The results of a mathematics placement exam at two different campuses of Mercy College follow:  Given that the two population standard deviations are known,what is the p-value?
A)1.0 
B)0.0 
C)0.05 
D)0.95

Quizplus · Accepted Answer

The p-value is defined as the probability of obtaining a sample statistic (in this case, the difference in means between two campuses) at least as extreme as the one observed, assuming the null hypothesis is true. Since the null hypothesis is that there is no difference in means between the two campuses, the p-value is the probability of obtaining a difference in means as large or larger than what was observed assuming no difference exists. Looking at the results, the difference between the means is 2.2 with a standard deviation of 0.9, and since the population standard deviations are known, a z-test can be used. Using a two-tailed z-test with alpha level of 0.05, the critical value is 1.96. The z-statistic for the observed difference in means is (2.2-0)/[sqrt((9^2/40)+(14^2/35))] which simplifies to 2.396, which falls into the rejection region. Therefore, the p-value is less than 0.05, and since it is smaller than the alpha level, the null hypothesis is rejected. Since the p-value is less than alpha, the answer is B, 0.0.

The Results of a Mathematics Placement Exam at Two Different