Question

Since an instant replay system for tennis was introduced at a major​ tournament, men challenged 1398 referee​ calls, with the result that 414 of the calls were overturned. Women challenged 762 referee​ calls, and 219 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. Test the claim using a hypothesis test. 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? Identify the test statistic. Identify the​ P-value. What is the conclusion based on the hypothesis​ test? Test the claim by constructing an appropriate confidence interval. The 95​% confidence interval is_(p1-p2)_ What is the conclusion based on the confidence​ interval?

Answer 1

Test and CI for Two Proportions

Method

p₁: proportion where Sample 1 = Event

p₂: proportion where Sample 2 = Event

Difference: p₁ - p₂

Descriptive Statistics

Sample	N	Event	Sample p
Sample 1	1398	414	0.296137
Sample 2	762	219	0.287402

Estimation for Difference

CI based on normal approximation

Test Hypothesis

Null hypothesis	H₀: p₁ - p₂ = 0
Alternative hypothesis	H₁: p₁ - p₂ ≠ 0

Method	Z-Value	P-Value
Normal approximation	0.43	0.6691

Test stats Z = 0.43

P-value = 0.6691

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95% CI =

Difference	95% CI for Difference
0.0087358	(-0.031329, 0.048801)

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c) Conclusion

We have enough evidence to conclude that the proportion of male and female who overturns number of Refree call are equal.