Suppose there is a claim that a certain population has a mean, $\mu$, that is different than 7 . You want to test this claim. To do so, you collect a large random sample from the population and perform a hypothesis test at the 0.05 level of significance. To start this test, you write the null hypothesis $H_{0}$ and the alternative hypothesis $H_{1}$ as follows.
\[
\begin{array}{l}
H_{0}: \mu=7 \\
H_{1}: \mu \neq 7
\end{array}
\]
Suppose you also know the following information.
The critical values are -1.960 and 1.960 (rounded to 3 decimal places).
The value of the test statistic is 2.245 (rounded to 3 decimal places).
(a) Complete the steps below to show the rejection region(s) and the value of the test statistic for this test.
Check
Save For Later
Submit Assic

Step 1 ：State the null hypothesis $H_{0}$: \(\mu = 7\) and the alternative hypothesis $H_{1}$: \(\mu \neq 7\).

Step 2 ：Identify the critical values for the test, which are -1.960 and 1.960.

Step 3 ：Identify the test statistic, which is 2.245.

Step 4 ：Determine the rejection region for a two-tailed test at the 0.05 level of significance. The rejection region is any value less than -1.960 or greater than 1.960.

Step 5 ：Compare the test statistic to the critical values. The test statistic of 2.245 is greater than the upper critical value of 1.960, so it falls into the rejection region.

Step 6 ：Since the test statistic falls into the rejection region, we reject the null hypothesis that the population mean is 7.

Step 7 ：\(\boxed{\text{Reject } H_{0}}\). Therefore, there is sufficient evidence to support the claim that the population mean is different from 7.