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 orfail 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 = .01significance level. At the end of the test you concluded to rejectthe null hypothesis. If you had instead used alpha = .10, would youhave rejected the null hypothesis, failed to reject the nullhypothesis, or is there not enough information? (reject, fail toreject, or not enough)

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

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

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

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

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

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

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