Question

15. Which of the following statements is true? a. If the calculated value of F statistic is higher than the critical value, we reject the alternative hypothesis in favor of the null hypothesis. b. The F statistic is always nonnegative as SSRr is never smaller than SSRur. c. Degrees of freedom of a restricted model is always less than the degrees of freedom of an unrestricted model. d. The F statistic is more flexible than the t statistic to test a hypothesis with a single restriction

Answer 1

c) is true

Explanation:

Given are four statements. Let us check one by one

a) If the calculated value of F statistic is higher than the critical value, we reject the alternative hypothesis in favor of the null hypothesis

False, we reject H0 in favour or alternate

b) The F statistic is always nonnegative as SSRr is never smaller than SSRur.

F statistics is non negative but reason is bot SSRr and SSRur are positive

Not because SSRr is never smaller than SSRur

c) Degrees of freedom of a restricted model is always less than the degrees of freedom of an unrestricted model.

This is true because in a restricted we put constraints thus df will be less

d) The F statistic is more flexible than the t statistic to test a hypothesis with a single restriction.

False. F statistic is for testing variances while t statistic for means.