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

==============================================

95% CI =

Difference | 95% CI for Difference |

0.0087358 | (-0.031329, 0.048801) |

============================================

c) Conclusion

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

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