The director of admissions of a distinguished MBA program is interested in studying the proportion of entering students in similar graduate business programs who have achieved a composite score on the Graduate Management Admissions Test (GMAT) in excess of 630. Specifically, the admissions director believes that the proportion of students entering top rated graduate programs with such composite GMAT scores is higher in 2016 than it was in 2012. To test this hypothesis, he has collected random samples of MBA candidates entering his program in the fall of 2016 and in the fall of 2012. He believes that these GMAT scores are indicative of the scores earned by their peers in his program and in competitors programs. The GMAT scores for the random students entering in each year are provided on the left

a. Test the director's claim at the alpha equal .05 level of significance placing the claim on the alternate hypothesis for a more stringent test.

b. Does the conclusion change when the significance level is decreased to 1%?

Data:

Student	GMAT2016	GMAT2012
1	606	625
2	626	624
3	613	612
4	619	622
5	621	604
6	625	626
7	641	604
8	621	608
9	635	597
10	609	633
11	616	611
12	618	606
13	628	621
14	617	615
15	630	628
16	651	620
17	614	610
18	619	609
19	623	637
20	645	605
21	648	623
22	632	612
23	636	616
24	640	630
25	630	624

Please, show step by step process

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