Q.7 - The Practice of Statistics for AP

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 $H_0 : \mu =2$ 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 $A=0.05$.

Step-by-Step Solution

Answer

The correct answer is (e).

Step 1: Given Information

$H_0:\mu =2$

$H_a:\mu \ne 2$

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

Step 2: 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 $H_0$.