A computerized tutorial center at a local college wants to compare two different statistical software programs. Students going to the center are matched with other student having similar abilities in statistics (assume the matching process creates matched pairs acceptable for use with the appropriate paired test statistic for the null hypothesis of no difference). A random sample of 10 student pairs is selected for each pair, one student is randomly assigned program A, the other program B. After two weeks of using the program, the students are given an evaluation test. Their grades are:
|
Program A
|
Program B
|
|
64
|
62
|
|
68
|
72
|
|
75
|
79
|
|
97
|
57
|
|
90
|
91
|
|
55
|
56
|
|
68
|
88
|
|
64
|
89
|
|
91
|
77
|
|
95
|
76
|
Do the data provide evidence, at the 5% significance level, that there is a difference in mean student performance between the two software programs? Assume that the population of all possible paired differences is approximately normally distributed. In support of your decision show the null and alternative hypothesis and the value of the test statistics computed for assessing the significance level.