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 \(t > \boxed{1.943}\).