The following data shows the marks for test and exam for a random sample of 12 STAT2013 students.

Student 1 2 3 4 5 6 7 8 9 10 11 12

Test 66 78 62 99 80 63 82 42 30 59 52 60

Exam 79 78 62 75 84 68 72 45 42 51 48 65

Assuming normality, does the data show differences on the average performances for the students taking STAT2013 in the test and exam. Use 5% level of significance.

(a) What is the standard error of the sample mean differences?

(b) What is the absolute test statistic?

(c) What is the absolute critical value?

(d) What is the p-value?

(e) The conclusion is that there insufficient evidence to show that the means are equal for the test and exam.(True/False)