Question

Since an instant replay system for tennis was introduced at a major tournament, men challenged 1425 referee calls with the results that 412 of the calls were overturned. Women challenged 739 referee calls, and 221 of the calls were overturned. Use a 0.05 significance level to test the claim that men and women have equal success in challenging calls. Test the claim using a hypothesis test. Consider the first sample to be the sample of male tennis players who challenge referee calls and the second sample to be the sample of female tennis players that challenged referee calls. What are the null and alternative hypotheses for the hypothesis test.

Answer 1

CI = (-0.0445, 0.0225)

there is no sufficient evidence to men and women have equal success in challenging calls

Explanation:

Sample size for men; n1 = 1425

Number of success for men; x1 = 412

Sample size for women; n2 = 739

Number of success for women; x2 = 221

Significance level; α = 0.05

Sample proportion for men;

p1 = x1/n1 = 412/1425

p1 = 0.2891

Sample proportion for women;

p2 = x2/n2 = 221/739

p2 = 0.2991

From tables, z-score at significance level of 0.05 is 1.96.

Formula for margin of error is;

E = z√[(p1(1 - p1)/n1) + (p2(1 - p2)/n2)]

Plugging in the relevant values;

E = 1.96√[(0.2891(1 - 0.2891)/1425) + (0.2991(1 - 0.2991)/1425)]

E = 1.96 × 0.0170687

E = 0.0335

Coordinates of the confidence interval will be;

[(p1 - p2) - E], [(p1 - p2) + E]

[(0.2881 - 0.2991) - 0.0335], [(0.2881 - 0.2991) + 0.0335]

CI = (-0.0445, 0.0225)

This means that the confidence interval contains 0 since it's between (-0.0445 and 0.0225). Thus we can conclude that there is no sufficient evidence to men and women have equal success in challenging calls