Question

2. Michael likes to bowl. He’s been alternating between two brands of shoes, A and B, and is trying to decide if the brand matters in his success. Suppose a spare or a strike counts as success, and an open frame counts as failure. The following table summarizes his stats:

a) Michael wants to know if he performs better with Brand A or Brand 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) Michael performs the test you recommended and finds a p-value of 0.126. What does this number mean? A: e) What does Michael learn from this test?

2. Michael likes to bowl. He's been alternating between two brands of shoes, A and B, and is trying to decide if the brand matters in his success. Suppose a spare or a strike counts as success, and an open frame counts as failure. The following table summarizes his stats: Brand A Number of successes50 36 Brand B 39 Number of failures 45

Answer 1

na = 50+36 = 86, Pa (proportion of success of Brand A) = 50/86 = 0.58
nb = 39+45 = 84, Pb (proportion of success of Brand B) = 39/84 = 0.46

Null Ho: Pa=Pb
Alternate: Ha: Pa not equal to Pb

pooled sample proportion:
p = (pa * na + pb * nb) / (na + nb) = 0.52

standard error:
sqrt{ p * ( 1 - p ) * [ (1/na) + (1/nb) ] } = 0.077

test statistic
z = (pa - pb) / SE
z = 1.53

p-value of 0.126 signifies the probability of the extreme results

p-value of 0.126 implies that the difference in success is not significant at 1%, 5% or 10% significance levels as the p-value is greater