A null hypothesis can only be rejected at the 5% significance level if and only if:
A) a 95% confidence interval includes the hypothesized value of the parameter
B) a 95% confidence interval does not include the hypothesized value of the parameter
C) the null hypothesis is biased
D) the null hypotheses includes sampling error

Question

Quizplus · Accepted Answer

The 5% significance level means that we will reject the null hypothesis if we obtain a result that is unlikely to have occurred by chance more than 5% of the time. This is equivalent to saying that if we construct a 95% confidence interval, and it does not include the hypothesized value of the parameter, we can reject the null hypothesis at the 5% significance level. Option A is incorrect because a confidence interval that includes the hypothesized value would fail to reject the null hypothesis. Option C is incorrect because the null hypothesis being biased is not a requirement for rejecting it, and Option D is incorrect because the null hypothesis including sampling error is a common occurrence and does not influence the decision to reject it.

A Null Hypothesis Can Only Be Rejected at the 5