Question

Joe is a baseball player. He’s been alternating between two brands of bats, A and B, and is trying to decide which one he should use for the rest of the season. To keep it simple, he either hits or strikes-out in each of his plate appearances. The following table summarizes his stats:

	Bat A	Bat B
Number of hits	33	55
Number of strike-outs	100	90

a)	Joe wants to know if he performs better with Bat A or Bat B. How would you state the hypothesis that he is testing?
A:

b)	What is the null hypothesis?
A:

c)	What statistical test should he use?
A:

d)	Joe performs the test you recommended and finds a p-value of 0.0188 What does this number mean?
A:

e)	What does Joe learn from this test?
A:

Answer 1

Answer for a)

Sa=Strike rate with A and Sb= Strike rate with B

Then Null Hypothesis is Sa>Sb

Alternate Hypothesis Sa>!Sb

We have sample size more than 30 then there is no harm in using z test

If p value is 0.0188 ie 1.88% and significance of test is 5% ie our calculated value of p is less than 5% hence we can reject null hypothesis considered.

Joe has rejected null hypothesis then he can predict that given this sample we have strike rate of B is either equal or greater than that of A in simple words performance of B is either as good as or better than A