Problem

Find the critical value(s) and rejection region(s) for the indicated t-test, level of significance $\alpha$, and sample size $n$.
Two-tailed test, $\alpha=0.10, n=7$
E Click the icon to view the t-distribution table.
The critical value(s) is/are $1.943,-1.943$
(Round to the nearest thousandth as needed. Use a comma to separate answers as needed.)
Determine the rejection region(s). Select the correct choice below and fill in the answer box(es) within your choice. (Round to the nearest thousandth as needed.)
B. $\square< \mathrm{t}< $
A. $t< \square$ and $t> \square$
D. $t> $
C. $\mathrm{t}< $

Answer

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Answer

Final Answer: The critical values are \(\boxed{1.943, -1.943}\). The rejection regions are \(t < \boxed{-1.943}\) and \(t > \boxed{1.943}\).

Steps

Step 1 :Given a two-tailed t-test with a level of significance of 0.10 and a sample size of 7.

Step 2 :The critical values are the points beyond which we reject the null hypothesis. For a two-tailed test, we have two critical values, one on the left and one on the right.

Step 3 :The critical values are found by looking up the t-value in a t-distribution table that corresponds to the desired level of significance and degrees of freedom. The degrees of freedom is calculated as the sample size minus 1.

Step 4 :The rejection regions are the areas under the curve of the t-distribution that are beyond the critical values. For a two-tailed test, there are two rejection regions, one on the left and one on the right.

Step 5 :Given that the level of significance is 0.10, the sample size is 7, and the degrees of freedom is 6, the critical value is 1.943.

Step 6 :The rejection regions are then calculated to be (-1.943, 1.943).

Step 7 :Final Answer: The critical values are \(\boxed{1.943, -1.943}\). The rejection regions are \(t < \boxed{-1.943}\) and \(t > \boxed{1.943}\).

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