Question

A random sample of 29 pairs of observation from a normal population gives correlation coefficient of 0.64. Is it likely that variables in the population are uncorrelated at 5% L.O.S?

Answer 1

Solution :

The null and alternative hypotheses are as follows :

i.e. The correlation coefficient between the variables in the population is equal to zero.

  i.e. The correlation coefficient between the variables in the population is not equal to zero.

To test the hypothesis we shall use t-test for testing the significance of correlation coefficient. The test statistic is given as follows :

Where, r is sample correlation coefficient and n is sample size.

We have, r = 0.64 and n = 29

The value of the test statistic is 4.3280.

Degrees of freedom = (n - 2) = (29 - 2) = 27

Since, our test is two-tailed test, therefore we shall obtain two-tailed p-value for the test statistic. The two-tailed p-value is given as follows :

p-value = 2.P(T > t)

p-value = 2.P(T > 4.3280)

p-value = 0.0002

The p-value is 0.0002

Level of significance = 5% = 0.05

(0.0002 < 0.05)

Since, p-value is less than the significance level of 5%, therefore we shall reject the null hypothesis at 5% significance level.

Conclusion : At significance level of 5%, we have sufficient evidence to conclude that, it is not likely that variables in the population are uncorrelated.

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