Question

After checking that conditions are met, you perform a significance test of $H_0:\mu =1$versus $H_{\alpha }:\mu \ne 1$. You obtain a $P$value of $0.022$. Which of the following is true?

(a) A$95\%$confidence interval for $\mu$will include the value $1$

(b) A $95\%$confidence interval for$\mu$will include the value $0$.

(c) A$99\%$ confidence interval for$\mu$will include the value $1$

(d) A $99\%$confidence interval for $\mu$will include the value $0$

(e) None of these is necessarily true.

Short answer

(c) A $99\%$ confidence interval for $\mu$will include the value $1$.

Step-by-step solution

Step-1 Given Information

Given In the question that,

The null and alternative hypothesis are:

$H_0:\mu =1$

$H_{\alpha }:\mu \ne 1$

$P-value=0.022$

we have to find the correct option.

Step-2 Explanation

The null hypothesis is rejected if $P$-value is less than the significance level, otherwise not. Here, $P$-value$\left(0.022\right)$is greater than the significance level$\left(\alpha =0.01\right)$. Thus, the null hypothesis is not rejected. Thus, it could be concluded that the $99\%$confidence interval would contain the value $\mu =1$.

Thus, the correct option is (c).