5 You estimate a simple linear regression model using a samp

5. You estimate a simple linear regression model using a sample of 25 observations and obtain the following results (estimated standard errors in parentheses below coefficient estimates): y = 97.25 + 19.74 *x (3.86) (3.42) You want to test the following hypothesis: H0: beta2 = 1, H1: beta2 >12. If you choose to reject the null hypothesis based on these results, what is the probability you have committed a Type I error? a.)between .01 and .02 b.)between .02 and .05 c.)less than .005 d.) It is impossible to determine without knowing the true value of beta2

Solution

Answer is c.)

Since t statistic is highly significant t= (beta_hat - beta_not)*sqrt(sample size)/standard error

Thus H0 is rejected

Type 1 error is probability of rejecting H0 when it is true.

& Is actiaact @ significance level

Thus t being highly significant , so p value is very less which equals the minimum significance level at which H0 is rejected.

So @ is less than .5 %