Question

Below are the average heights for American boys. Consider “birth” to be 0 years old.

Age (years)	Height (cm)
birth	50.8
2	83.8
3	91.4
5	106.6
7	119.3
10	137.1
14	157.5

c) Find the correlation coefficient r. (Round your answer to four decimal places.) Is it significant at the 0.01 level? If so why?

Answer 1

(i)

X       Y              XY              X²                   Y²

0       50.8           0                0                     2580.64

2       83.8          167.6          4                      7022.44

3       91.4          274.2          9                      8353.96

5       106.6         533            25                   11363.56

7       119.3         835.1          49                  14232.49

10       137.1      1371            100                 18796.41

14        157.5      2205           196                  24806.25

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41         746.5      5385.9       383                     87155.75

(ii)

Test statistic is:

t = r/SE

= 0.9761/0.0972 = 10.0422

= 0.01

ndf = n - 2 = 7 - 2 = 5

From Table, critical values of t = 4.0321

Since the calculated value of t is greater than critical value of t, Reject H0.

Conclusion:

It is significant at 0.01 level.