Question

Significance tests A test of H0: p = 0.65 against Ha: p < 0.65 has test statistic z = −1.78. (a) What conclusion would you draw at the 5% significance level? At the 1% level? (b) If the alternative hypothesis were Ha: p ≠ 0.65, what conclusion would you draw at the 5% significance level? At the 1% level?

Answer 1

Answer:

(a) At 5% significance level, reject H0

At 1% significance level, reject H0

(b) At 5% significance level, fail to reject H0

At 1% significance level, fail to reject H0

Step-by-step explanation:

(a) The test is a one tailed test

At 5% significance level, the critical value is 1.645

Conclusion: Reject H0 because the test statistic -1.78 is less than the critical value 1.645

At 1% significance level, the critical value is 2.326

Conclusion: Reject H0 because the test statistic -1.78 is less than the critical value 2.326

(b) The test is a two tailed test

At 5% significance level, the critical value is 1.96. The region of no rejection of H0 lies between -1.96 and 1.96

Conclusion: Fail to reject H0 because the test statistic -1.78 falls within -1.96 and 1.96

At 1% significance level, the critical value is 2.576. The region of no rejection of H0 lies between -2.576 and 2.576

Conclusion: Fail to reject H0 because the test statistic falls within -2.576 and 2.576