Question

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.

Group of answer choices

Answer 1

The critical values of the hypothesis test is Z = ±1.96

Using α = 0.05 ; for a two tailed test where the null and Alternative hypothesis are defined as ;

`H_(0) : p_(1) = p_(2)`

`H_(1) : p_(1) ≠ p_(2)`

A two-tailed test, also known as a non-directional or two-sided test, is a type of hypothesis testing used to determine whether there is a statistically significant difference along both sides. This means the critical region could lie on either side of the mean or proportion given. Hence, to the value covers both the left and right right area of the curve.

Now we have ;

• α = 0.05/2 = 0.025

The Zscore at P( z < 0.025) or P(z > 0.025) = ±1.96

Hence, the critical values for the hypothesis test is Z = ±1.96