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 7/9 referee calls, and... 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. ( 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 greater than the significance level of ( alpha = 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.

b. test the claim by constructing an appropriate confidence interval.
the 95% confidence interval is ( - 0.018 < (p_1 - p_2) < 0.062 ) (round to three decimal places as needed.)

what is the conclusion based on the confidence interval?
because the confidence interval limits 0, there appear to be a significant difference between the two proportions. there evidence to warrant rejection of the claim that men and women have equal success in challenging calls.

Explanation:

Step1: Identify Hypotheses

The claim is men and women have equal success in challenging calls, so null hypothesis \( H_0: p_1 = p_2 \), alternative \( H_1: p_1
eq p_2 \) (matches option D).

Step2: Test Statistic

Given \( z = 1.08 \) (from problem, no calculation needed here).

Step3: P - value

Given \( P\text{-value} = 0.280 \) (rounded as needed).

Step4: Hypothesis Test Conclusion

Since \( P\text{-value} = 0.280 > \alpha = 0.05 \), fail to reject \( H_0 \). Insufficient evidence to reject the claim (equal success).

Step5: Confidence Interval Conclusion

95% CI for \( p_1 - p_2 \) is \( -0.018 < (p_1 - p_2) < 0.062 \). Since 0 is in the interval, no significant difference. So no sufficient evidence to reject 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: Fail to reject \( H_0 \), insufficient evidence.

b. Confidence Interval Conclusion: 0 is in the interval, so no significant difference. No sufficient evidence to reject the claim that men and women have equal success.