Question

Since an instant replay system for tennis was introduced at a major​ tournament, men challenged 1404 referee​ calls, with the result that 414 of the calls were overturned. Women challenged 748referee​ calls, and 214 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. Complete parts​ (a) through​ (c) below.

1) Consider the first sample to be the sample of male tennis players who challenged referee calls and the second sample to be the sample of female tennis players who challenged referee calls. What are the null and alternative hypotheses for the hypothesis​ test?

2)Identify the test statistic.

3)Identify the​ P-value.

4)What is the conclusion based on the hypothesis​ test?

5) The 95​% confidence interval is

6)What is the conclusion based on the confidence​ interval?

7)Based on the​ results, does it appear that men and women may have equal success in challenging​ calls?

Answer 1

a) As we are testing here whether the two proportions are equal, therefore the null and the alternative hypothesis here are given as:

b) The pooled proportion here is computed as:
P = (x₁ + x₂) / (n₁ + n₂) = (414 + 214) / (1404 + 748) = 0.2918

The standard error thus is computed here as:

The sample proportions are computed here as:
p₁ = 414 / 1404 = 0.2949
p₂ = 214/748 = 0.2861

Therefore the test statistic now is computed here as:

Therefore 0.43 is the required test statistic value here.

c) As this is a two tailed test, the p-value here is computed from the standard normal tables as:
p = 2P( Z > 0.43) = 2*0.3351 = 0.6702

Therefore 0.6702 is the required p-value here.

Q4) As the p-value here is 0.6702 > 0.05 which is the level of significance, therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we dont have sufficient evidence to reject the claim here.

Q5) From standard normal tables, we have:
P(-1.96 < Z < 1.96) = 0.95

Therefore the confidence interval here is computed as:

this is the required 95% confidence interval here.

Q6) As the confidence interval obtained contains 0, therefore the there is no significant difference between the two proportion here.

Q7) Yes, we dont have enough evidence to reject the claim that men and women have equal success in challenging calls.