Question

4. Hockey 2018 During the 2018 National Hockey League playoffs, the home team won 41 of the 85 games played. Assume this represents a random sample of hockey games. Is this strong evidence of a home-ice disadvantage (the home teams win less than 50% of the time) in professional hockey? a. Verify the sample is large enough to use procedures based on the normal distribution. b. What do you conclude? Support your conclusion by testing an appropriate hypothesis using a p-value.

Answer 1

a) The sample proportion here is computed as:

p = 41/85 = 0.4824

Here we have np = 41 and n(1-p) = 85 - 41 = 44, which are both large enough to conclude that the sample is large enough to allow for normal distribution assumption.

b) The test statistic here is computed as:

As this is a one tailed test, the p-value here is computed as:

p = P(Z < -0.3254 ) = 0.3724

Therefore 0.3724 is the p-value here.

As the p-value here is large enough, we cannot reject the null hypothesis here, we dont have sufficient evidence here to reject the null hypothesis.