Question

Solve the problem.

The table shows the number of pitchers with E.R.A's below 3.5 in a random sample of sixty pitchers from the National League and in a random sample of fifty-two pitchers from the American League. Assume that you plan to use a significance level of α = 0.05 to test the claim that Find the critical value(s) for this hypothesis test.

Answer 1

The critical value(s) of the hypothesis test is Z = ± 1.96

The test given is a two-tailed test , which means that the test for sigbificance is in both directions as opposed to that of a one-tailed test.

Unlike a one-tailed test where the critical region lies only on one side of the distribution (e.g., right tail for "greater than"), a two-tailed test has two critical regions, one on each side of the distribution (e.g., left and right tails). These regions represent the values of the test statistic that are unlikely to occur under the assumption of the null hypothesis

Here, α = 0.05

• α = 0.05/2 = 0.025

P(Z = 0.025) = ±1.96

Hence , the critical value(s) for the hypothesis test is Z = ±1.96