Question

1) Use these two confidence intervals to answer the question. 90%: (0.770, 0.808) and 99%: (0.759, 0.818)

If H_0: pi = .81 and H_a: pi not equal to .81, do we reject or fail to reject the null hypothesis at the alpha = .01 level? (reject or fail to reject)

2) Suppose you conducted a significance test with an alpha = .01 significance level. At the end of the test you concluded to reject the null hypothesis. If you had instead used alpha = .10, would you have rejected the null hypothesis, failed to reject the null hypothesis, or is there not enough information? (reject, fail to reject, or not enough)

3) Suppose you conducted a significance test with an alpha = .10 significance level. At the end of the test you concluded to reject the null hypothesis. If you had instead used alpha = .01, would you have rejected the null hypothesis, failed to reject the null hypothesis, or is there not enough information? (reject, fail to reject, or not enough)

Let n = 100, p_hat = .35, H_0: pi = .25, H_a: pi > .25, and alpha = .05. Use this information to answer 4), 5) , and 6).

4) If p_hat = .4 and everything else stayed the same, would the power increase or decrease?

5) If alpha = .01 and everything else stayed the same, would the power increase or decrease?

6) If n = 50 and everything else stayed the same, would the power increase or decrease?

7) If alpha = .01 and the p-value is .0144, what type of error is possible in this test? (type I or type II)  (Hint: you need to first think about the test decision)

8) If alpha = .05 and the p-value is .0144, what type of error is possible in this test? (type I or type II)  (Hint: you need to first think about the test decision)

Answer 1

1) Use these two confidence intervals to answer the question. 90%: (0.770, 0.808) and 99%: (0.759, 0.818)

If H_0: pi = .81 and H_a: pi not equal to .81, we fail to reject the null hypothesis at the alpha = .01 level becasue 0.81 is inside 99% CI

2) Suppose you conducted a significance test with an alpha = .01 significance level. At the end of the test you concluded to reject the null hypothesis. If you had instead used alpha = .10, we reject the null hypothesis, at alpha = .10.

3) Suppose you conducted a significance test with an alpha = .10 significance level. At the end of the test you concluded to reject the null hypothesis. If you had instead used alpha = .01, there not enough information.

Let n = 100, p_hat = .35, H_0: pi = .25, H_a: pi > .25, and alpha = .05. Use this information to answer 4), 5) , and 6).

4) If p_hat = .4 and everything else stayed the same, the power decrease

5) If alpha = .01 and everything else stayed the same, the power increase

6) If n = 50 and everything else stayed the same, would the power decrease

7) If alpha = .01 and the p-value is .0144, what type of error is possible in this test ,type 1 error

8) If alpha = .05 and the p-value is .0144, what type of error is possible in this test , type II error