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?

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Mathematics

Dulce Mullins

6 March, 07:58

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?

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Nickolas Trevino · Answer 1

(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