You wish to test the following claim $($

H

a

$)$ at a significance level of

$\backslash$alpha

$=$

$0\mathrm{.}10$

$.$

H

o

:

$\backslash$mu

$=$

$86\mathrm{.}5$

H

a

:

$\backslash$mu

$!=$

$86\mathrm{.}5$

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size

n

$=$

$312$

with mean

$$

x

$=$

$85\mathrm{.}8$

and a standard deviation of

s

$=$

$8\mathrm{.}3$

$.$

What is the test statistic for this sample? $($Report answer accurate to three decimal places.$)$

test statistic $=$

What is the p$-$value for this sample? $($Report answer accurate to four decimal places.$)$

p$-$value $=$

The p$-$value is$...$

less than $($or equal to$)$

$\backslash$alpha

greater than

$\backslash$alpha

This test statistic leads to a decision to$...$

reject the null

accept the null

fail to reject the null

As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to $86\mathrm{.}5.$

There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to $86\mathrm{.}5.$

The sample data support the claim that the population mean is not equal to $86\mathrm{.}5.$

There is not sufficient sample evidence to support the claim that the population mean is not equal to $86\mathrm{.}5.$