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. A random sample of 10 student pairs is selected. 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 10% significance level, that there is a difference in mean student performance between the two software programs?
a) In support of your decision show the hypotheses and the value of the test statistics computed for assessing the significance level.
b) What is the actual type 1 error?