Question

In: Statistics and Probability

Male students at SCC last semester. You will use this data throughout the semester on your...

Male students at SCC last semester. You will use this data throughout the semester on your lab assignments.

Student # Gender Height Shoe Age Hand

1 M 67 10 19 R

2 M 74 12 17 R

3 M 72 11.5 19 R

4 M 69 10 35 R

5 M 66 9 18 R

6 M 71 10.5 17 R

7 M 72 10.5 17 R

8 M 66 10 20 R

9 M 67 10 18 R

10 M 71 10.5 24 R

11 M 66 10 21 R

12 M 71 10.5 18 R

13 M 69 10 22 R

14 M 66 9.5 18 L

15 M 76 14 18 R

16 M 69 11 22 R

17 M 68 9 19 R

18 M 70 12 30 R

19 M 67 10 24 R

20 M 70 11 21 R

21 M 70 10 52 R

22 M 63 9 27 R

23 M 69 11 22 R

24 M 72 10 22 R

25 M 76 11.5 20 L

26 M 75 11 17 R

27 M 72 11 50 L

28 M 69 11 20 R

29 M 70 12 20 R

30 M 69 11.5 23 R

31 M 70 11 18 R

32 M 67 10 21 R

33 M 68 11 44 R

34 M 76 13 48 R

35 M 62 8 23 L

36 M 69 9 19 R

37 M 72 10 60 R

38 M 73 11.5 41 R

39 M 70 9.5 39 R

40 M 78 15 24 R

41 M 65 8.5 23 R

42 M 68 9.5 20 R

2. Using the SCC men’s/women’s class sample data at the ?=0.05, is there enough evidence to conclude that there is a significant linear correlation between men’s/women’s height and men’s/women’s shoe size?

a. State the null and alternate hypotheses.

b. Specify the level of significance.

c. State the correlation coefficient. (3 decimal places)

d. State the critical value from Table 11. (Use the value of n that is closest to your sample size.)

e. State whether to “reject the ?0” or “fail to reject the ?0”.

f. Interpret the decision in the context of the original claim.

Solutions

Expert Solution

Let us first calculate the corerlation coefficient first. In order to calculate this, we need the squraes, cross products and their total. We shall make use of the table below in calculating the correlation.

Gender Height Shoe X^2 y^2 X*Y
M 67 10 4489 100 670
M 74 12 5476 144 888
M 72 11.5 5184 132.25 828
M 69 10 4761 100 690
M 66 9 4356 81 594
M 71 10.5 5041 110.25 745.5
M 72 10.5 5184 110.25 756
M 66 10 4356 100 660
M 67 10 4489 100 670
M 71 10.5 5041 110.25 745.5
M 66 10 4356 100 660
M 71 10.5 5041 110.25 745.5
M 69 10 4761 100 690
M 66 9.5 4356 90.25 627
M 76 14 5776 196 1064
M 69 11 4761 121 759
M 68 9 4624 81 612
M 70 12 4900 144 840
M 67 10 4489 100 670
M 70 11 4900 121 770
M 70 10 4900 100 700
M 63 9 3969 81 567
M 69 11 4761 121 759
M 72 10 5184 100 720
M 76 11.5 5776 132.25 874
M 75 11 5625 121 825
M 72 11 5184 121 792
M 69 11 4761 121 759
M 70 12 4900 144 840
M 69 11.5 4761 132.25 793.5
M 70 11 4900 121 770
M 67 10 4489 100 670
M 68 11 4624 121 748
M 76 13 5776 169 988
M 62 8 3844 64 496
M 69 9 4761 81 621
M 72 10 5184 100 720
M 73 11.5 5329 132.25 839.5
M 70 9.5 4900 90.25 665
M 78 15 6084 225 1170
M 65 8.5 4225 72.25 552.5
M 68 9.5

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