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 for testing the claim
`p_1\\eq p_2` at a significance level of 0.05 is z=±1.96.

To calculate the critical values for the test of the claim
`p_1\\eq p_2` at a significance level of 0.05, we use the standard normal distribution. The critical values are determined by the chosen significance level and the fact that it is a two-tailed test.

Given the significance level (α) of 0.05, which corresponds to a 95% confidence level, we look for the critical values that capture the middle 95% of the standard normal distribution. The critical values for a two-tailed test at this confidence level are z=±1.96.

Therefore, the critical values for the hypothesis test are z=−1.96 and z=1.96. If the calculated test statistic falls beyond these values, we would reject the null hypothesis in favor of the alternative hypothesis, suggesting that the proportions of pitchers with E.R.A.s below 3.5 in the National League and the American League are not equal.