Question

Cougar Forest is considered by many to be the best female golfer of all time. During her 20’s and 30’s, her average score was 69.7 strokes. Consider the 35 rounds she has currently played in her 40’s. The mean score of those rounds is 70.7 strokes with a standard deviation of 2.1 strokes. Assume these rounds represent a random sample.

(a) Is there evidence at the α = 0.05 significance level to conclude Cougar’s mean score is different in her 40’s?

(b) Interpret the P-value in the context of this test.

(c) Explain what a Type I error would mean in the context of this test.

(d) Explain what a Type II error would mean in the context of this test.

Answer 1

Interpretation: p-value is the probability of obtaining test statistics extreme than the one observed when the null hypothesis is true.

Type I error: We conclude Cougar’s mean score is not equal to 69.7 whereas Cougar’s mean score was 69.7

Type II error: We conclude Cougar’s mean score was 69.7 when Cougar’s mean score was different from 69.7