AM -vs- PM sections of Stats - Significance test (RawData, Software Required):
There are two sections of statistics, one in the afternoon (PM)with 30 students and one in the morning (AM) with 22 students. Eachsection takes the identical test. The PM section, on average,scored higher than the AM section. The scores from each section aregiven in the table below. Test the claim that the PM section didsignificantly better than the AM section, i.e., isthe difference in mean scores large enough to believe thatsomething more than random variation produced this difference. Usea 0.01 significance level.

(a) Use software to calculate the test statistic. Do not 'pool' thevariance. This means you do not assume equal variances. Round your answer to 2 decimal places. t = (b) Use software to get the P-value of the test statistic.Round to 4 decimal places. P-value = (c) What is the conclusion regarding the null hypothesis? reject H0fail to rejectH0     (d) Choose the appropriate concluding statement. The difference in mean scores is large enough to suggest thisdifference is due to something more than random variation.There isnot a big enough difference in mean scores to suggest that thisdifference is anything more than a result of randomvariation.     We have proven thatstudents in PM sections of statistics do better, on average, thanstudents taking AM sections.We have proven that there is nodifference between AM and PM sections of statistics.    Â

     PMScores (x1) AMScores (x2) 80 74 68 62 98 91 93 90 66 59 84 79 57 50 65 61 52 46 80 76 70 65 82 78 88 81 98 92 74 69 76 69 83 80 86 79 82 79 50 43 95 89 65 61 61 65 72 72 100 87 79 72