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.
$$\begin{array}{l}{H}_0:\mu =7\\ H_1:\mu \ne 7\end{array}$$
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.
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Step 1 ：State the null hypothesis $H_0$: $\mu =7$ and the alternative hypothesis $H_1$: $\mu \ne 7$.

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 ：$\boxed{{\displaystyle \text{Reject }{H}_0}}$. Therefore, there is sufficient evidence to support the claim that the population mean is different from 7.