Question

A $95\%$confidence interval for a population mean is calculated to be $(1.7,3.5)$. Assume that the conditions for performing inference are met. What conclusion can we draw for a test of role="math" localid="1650275427722" $H_0:\mu =2$versus $Ha:\mu \ne 2$at the $A=0.05$level based on the confidence interval?

(a) None. We cannot carry out the test without the original data.

(b) None. We cannot draw a conclusion at the $A=0.05$level since this test is connected to the $97.5\%$confidence interval.

(c) None. Confidence intervals and significance tests are unrelated procedures.

(d) We would reject $H_0$at level $A=0.05$.

(e) We would fail to reject $H_0$at level $A=0.05$.

Short answer

The correct answer is (e).

Step-by-step solution

Given Information

$H_0:\mu =2$

$H_a:\mu \ne 2$

$95\%$confidence interval: $(1.7,3.5)$.

Explanation

The confidence interval contains the value $2$ , the value $2$ is a likely candidate for the population mean $\mu$ and thus we fail to reject the null hypothesis $H_0$.