Question

Results of 99​% confidence intervals are consistent with results of​ two-sided tests with which significance​ level? Explain the connection. A 99​% confidence interval is consistent with a​ two-sided test with significance level alphaequals nothing because if a​ two-sided test with this significance level does not reject the null​ hypothesis, then the confidence interval ▼ contains does not contain the value in the null hypothesis.

Answer 1

Yes, they are consistent.

A 99​% confidence interval is consistent with a​ two-sided test with significance level alpha=0.01 because if a​ two-sided test with this significance level does not reject the null​ hypothesis, then the confidence interval does contains the value in the null hypothesis.

Explanation:

Yes, they are consistent.

A 99​% confidence interval is consistent with a​ two-sided test with significance level alpha=0.01 because if a​ two-sided test with this significance level does not reject the null​ hypothesis, then the confidence interval does contains the value in the null hypothesis.

The critical values of the confidence level are equivalent to the critical values in the hypothesis test. In the case that the conclusion of the test is to not reject the null hypothesis, the test statistic falls within the acceptance region: its value is within the critical values of the two-sided test.

Then, it is also within the critical values of the confidence interval and the sample mean (or other measure) will be within the confidence interval bounds.