Question

If the R-square of the simple regression of Y on X is 0.5, then the hypothesis that X doesnot have statistically significant effect on Y …… at the 5% level of significance.

		might be accepted or rejected
		is accepted
		is rejected
		can not be tested

Answer 1

Soluion: In order to test the above question, the method is to construct our null and alternative hypotheses as:

H0: rho = 0 vs Ha: rho not equal to 0 where rho is the population correlation coefficient
The test statistic to answer the given question is T=r*sqrt(n-2)/sqrt(1 -(r*r)) where r is the sample correlation coefficient and n is the sample size, sqrt refers to the square root function.

Here r is obtained by square root of R.
We reject H0 iff|T(observed)| > t(alpha/2,(n-2)) where t(Alpha/2,(n-2)) is the upper alpha/2 point of a Student's t distribution with (n-2) degrees of freedom. Or if p-value for the test statistics is less than the level of significance, alpha.

In both cases, we need the sample size to calculate the critical value or p-value.

Since the sample size is not given, he hypothesis that X doesnot have statistically significant effect on Y at the 5% level of significance.can not be tested.

Option (iv) is correct.