In: Statistics and Probability
Your friend Ande plays a lot of Overwatch, and mainly plays as one of two types of characters: Tank characters and Support characters. Suppose he grabs a random sample of 100 games where he played as a Tank character, which he won 63 of. He also takes a random sample of 150 games where he played as a Support character, which he won 75 of.
a) What is the estimate of the difference in proportion of games Ande wins? Find the estimate of pT ank − pSupport. b) Is it appropriate to assume that the sampling distribution of the difference in proportions is normally distributed?
c) Find a 95% confidence interval for the difference in part (a) and interpret it.
d) Suppose Ande wants to test to see if he wins a higher proportion of games as a Tank character at a significance level of .05. What are the hypotheses for this test?
e) Calculate the z-test statistic for the tests defined in part (d).
f) Find the P-value for the test defined in part (d)
g) State your conclusion for the hypothesis test, and then interpret the result in the context of the problem.