Question

Suppose that over the past 30 years during any given week of the major-league season, an average of µ = 12 players are hit by wild pitches. Assume that the distribution is normal with a standard deviation of σ =3. For a sample of n = 4 weeks, in which the daily temperature was extremely hot, the weekly average of hit-by- pitch players was M = 15.5.

Are players more likely to get hit by pitches during hot weeks? Use a one-tailed test with α = .05.

A)The null hypotheses in words is:

B)The alternative hypothesis in symbols is:

C)The critical z value is

D)The z-score statistic is:

E)Your decision is

F) Compute Cohen’s d to estimate the size of the effect.

Cohen's d is:

Answer 1

A) H₀: = 12

B) H₁: > 12

C) At = 0.05, the critical value is z_0.95 = 1.645

D) The test statistic z = ()/()

                                  = (15.5 - 12)/(3/)

                                  = 2.33

E) Since the test statistic value is greater than the critical value(2.33 > 1.645), so we should reject the null hypothesis.

F) Cohen's d = (M - )/

                      = (15.5 - 12)/3

                      = 1.167