justice. The sample mean response was $5\mathrm{.}12,$ and the sample standard deviation was $1\mathrm{.}38.$

a$.$ Test at the $1\%$ significance level, against a two$-$sided alternative, the null hypothesis that the population mean is $5.$

b$.$ Find the probability of a $1\%-$level test not rejecting the null hypothesis when the true mean response is $4\mathrm{.}85.$

Click the icon to view the standard normal distribution table.

a$.$ What are the null and alternative hypotheses for this test?

A$.H_0$:$5$

$H_1$:$>5$

c$.$

$H_0$:$5$

$H_1$:$<mn\; id="EditorElement\_1993123">5</mn>$

B$.$

$H_0$:$=5$

$H_1$:$5$

D$.$

$H_0$:$=5$

$H_1$:$=5\mathrm{.}12$

A$.$ Reject $H_0$ if or reject $H_0$ if $\frac{(\stackrel{}{x})-{}_0}{\frac{}{\sqrt[\phantom{2}]{n}}}>z_{\frac{}{2}}$

B$.$ Reject $H_0$ if

C$.$ Reject $H_0$ if $\frac{(\stackrel{}{x})-{}_0}{\frac{}{\sqrt[\phantom{2}]{n}}}>z_{}$

Determine the value for $-z_{},z_{},$ or $+-z_{\frac{}{2}}$ as appropriate for this test.

$($Round to two decimal places as needed. Use a comma to separate answers as needed.$)$