A sample of 15 students received the grades on midterm and final examinations in a statistics course as per provided in Table 12.

Table 12

Students' Grade on the Midterm and the Final Examinations in the Natural Scale

Table 13

Students' Grade on the Midterm and the Final Examinations in the Ordinal Scale

Midterm	Final
100	85
95	70
90	100
85	90
80	65
75	95
70	80
65	45
60	75
55	60
50	35
45	30
40	50
35	55
30	40

Midterm	Final
1	4
2	7
3	1
4	3
5	8
6	2
7	5
8	12
9	6
10	9
11	14
12	15
13	11
14	10
15	13

Use the sample data provided in Tables 12 and 13 to answer the following questions:

1. Evaluate the Pearson correlation between the two scores manually.The same scores are given in the rank scale in Table 13, calculate the rank correlation between the two scores manually, and comment on the result in both cases.

a. Discuss how the two correlations compare with each other.

2. Suppose that a sample ofthree (3) pairs is drawn from a population of pairs and elements of the sample are ranked. Construct the distribution of the statistic for testing the null hypothesis that the rank correlation between the two variables of the pair is 0. If = 0.05 what is(are) the critical value(s), what is the criterion for rejecting the null hypothesis, and how the p value is determined?