Question

1a. Suppose the value a is inside the 90% confidence interval for a coefficient in an estimated regression. Suppose one were to test the hypothesis that the coefficient is equal to a against the two sided alternative that it is not equal to a. Which of the following is a correct statement?

I would not reject the null at the 10% significance level

I would reject the null hypothesis at the 5% level of significance

I would reject the null hypothesis at the 1% level of significance

I would not reject the null hypothesis at the 5% level of significance

1b. Suppose a hypothesized slope value is not contained in the 95% confidence interval. If one were test the hypothesis at the 10% level which of the following statements are correct?

I would reject the null hypothesis

I would not reject the null hypothesis

I need more information

1c. An estimated regression coefficient is equal to 0.5. What is the confidence level associated with the one sided interval(0.5,∞)?

50%

95%

100%

90%

Answer 1

1a) I would not reject the null at 10% significance level

If the P value is more than significant level then you would fail to reject null hypothesis.

1b) I would reject the null hypothesis

If there is no hypothesize parameter then weshould reject the null hypothesis.When ever P value is low the null hypothesis is rejected.In this null hypothesis coefficient is zero.

1c) 95%

In a hypothesis test 5% level cannot be rejected.To attain true value the interval has probability function of 95%That means the confidence interval consisrs of true population mean.