Question

since an instant replay system for tennis was introduced at a major tournament, men challenged 1394 referee calls, with the result that 417 of the calls were overturned. women challenged 779 referee calls, and 216 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.

a. 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?
a. ( h_0: p_1 geq p_2 ) ( h_1: p_1
eq p_2 )
b. ( h_0: p_1 = p_2 ) ( h_1: p_1 > p_2 )
c. ( h_0: p_1
eq p_2 ) ( h_1: p_1 = p_2 )
d. ( h_0: p_1 = p_2 ) ( h_1: p_1
eq p_2 )
e. ( h_0: p_1 leq p_2 ) ( h_1: p_1
eq p_2 )
f. ( h_0: p_1 = p_2 ) ( h_1: p_1 < p_2 )
identify the test statistic.
( z = 1.08 ) (round to two decimal places as needed.)
identify the p - value.
p - value = 0.280 (round to three decimal places as needed.)
what is the conclusion based on the hypothesis test?
the p - value is the significance level of ( alpha = 0.05 ), so the null hypothesis. there evidence to warrant rejection of the claim that women and men have equal success in challenging calls.

Explanation:

Step1: Identify Hypotheses

The claim is that men and women have equal success in challenging calls, so the null hypothesis \( H_0: p_1 = p_2 \) (where \( p_1 \) is men's success proportion, \( p_2 \) is women's) and alternative \( H_1: p_1
eq p_2 \). So option D is correct.

Step2: Test Statistic

Given \( z = 1.08 \) (from the problem).

Step3: P - value

Given \( P\text{-value} = 0.280 \) (from the problem).

Step4: Conclusion

Compare \( P\text{-value} = 0.280 \) with \( \alpha = 0.05 \). Since \( 0.280>0.05 \), we fail to reject the null hypothesis. So there is not sufficient evidence to warrant rejection of the claim.

Answer:

a. Hypotheses: D. \( H_0: p_1 = p_2 \), \( H_1: p_1
eq p_2 \)
Test statistic: \( z = 1.08 \)
P - value: \( 0.280 \)
Conclusion: The P - value is \( 0.280 \) (greater than \( 0.05 \)), so fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that women and men have equal success in challenging calls.