Question

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 void
(D) the null hypotheses includes sampling error

Answer 1

Answer:

Option (B) a 95% confidence interval does not include the hypothesized value of the parameter              

Step-by-step explanation:

Alpha, α = 0.05

We conduct a hypothesis test at 5% significance level.

The null hypothesis will be rejected when

Option (B) a 95% confidence interval does not include the hypothesized value of the parameter

• When a 95% confidence interval is constructed,it contains all the possible values for the parameter being estimated.

• If the value of the parameter stated in the null hypothesis is contained in the 95% confidence interval, then we fail to reject the null hypothesis 0.05 level and accept it.

• If the value stated in the null hypothesis is not in the interval, then we fail to accept the null hypothesis and reject the null hypothesis at the 0.05 level.