A. Do we reject the null hypothesis that the intercept is zero at the 5% level a

Question

A. Do we reject the null hypothesis that the intercept is zero at the 5% level against the alternative that the coefficient is not equal to zero ? Do we reject the null hypothesis that the intercept is zero at the 5% level against the alternative that the coefficient exceeds zero ? Do we reject the null hypothesis that the intercept is zero at the 5% level against the alternative that the coefficientis less than zero ? (Answer “yes” or “no” to all three questions)

B. Answer the previous question, but now use the 1% significance level.

C. How can we know right away that the p-value that was deleted had to be greater than 5% ?

D. Can you deduce how big approximately the deleted p-value was?

Regression output Dependent Variable: tax89 Method: Least Squares Date: 10/17/17Time: 21:45 Sample: 1 30 Included observations: 30 Variable Coefficient Std. Error t-Statistic Prob. -. 1085026 2265805 0628626 0100449 inc89 22.56 0.000 0.9478 460 S.E. of regression 1434.561 Sum squared resid 522634209 -432.8308 Durbin-Watson stat 1.798742 R-squared Adjusted R-squared 0.9 Mean dependent var S.D. dependent var Akaike info criterion 17.43323 Schwarz criterion F-statistic Prob(F-statistic) 17.54795 508.81 0.0000 Log likelihood

Explanation / Answer

Answer to the questions:

The t value is -1.73 for the intercept. The hypothesis tested is

Ho: Beta = 0,
Ha: Beta !=0.

The P-Value is .094261.
The result is not significant at p < .05.

So, we do not reject null hypothesis. meaning B=0

A. Do we reject the null hypothesis that the intercept is zero at the 5% level against the alternative that the coefficient is not equal to zero ?

No, we don't reject the null hypothesis and conclude that the intercept is 0 for a 5% level signifiance. Our p-value is more than .05 at .0942 indicating intercept is not statistically significant.

Do we reject the null hypothesis that the intercept is zero at the 5% level against the alternative that the coefficient exceeds zero ?

No. Since the p-value is more than .05 we do not reject null hypothesis of this statement

Do we reject the null hypothesis that the intercept is zero at the 5% level against the alternative that the coefficientis less than zero ?

The P-Value is .047131.The result is significant at p < .05. So we reject the null hypothesis that the intercept is zero at the 5% level against the alternative that the coefficientis less than zero

B. For none of the cases, p-value is less than .01, and hence in none of statement you will reject the null hypothesis

C. You can know if p-value is bigger than .05 t statisitc is more than 2.045 in magnitude. Since 1.73 is less in magnitude than 2.045 ( for a df of 29 and 2 tailed .05 value), we can say that p-value will be more than .05

D. Yes. it is .0942

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