Question

1)

You compare the height and weight of 5 adult women. You get the following results:

height     weight

60           121

67           143

62           131

70           153

66           138

Perform a complete test of the hypothesis that the population correlation coefficient (ρ) is 0. Show all steps (note - obviously this should be a one sided test! Make sure you know why!)

Answer 1

Here we have to test, H0: = 0 against H1: > 0.

The test-statistic is given by, T = , where, r = sample correlation co-efficient = 0.9873, n = 5.

Hence, T = 10.7641.

Under H0, T ~ t-distribution with (n-2) d.f. i.e. 3 d.f.

The p-value = P(T > 10.7641) = 0.0009

Since, p-value < level of significance = 0.05 (assuming 5% level of significance), we reject the null hypothesis H0.

We conclude that the correlation co-efficient is significantly more than 0.