Question

Since an instant replay system for tennis was introduced at a major tournament, men challenged 1398 referee calls, with the result that 423 of the calls were overturned. Women challenged 771 referee 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. 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? OB. Ho-P1 = P2 H: P1 P2 OC. Ho-P1 = P2 HP1>P2 O A. Ho: P1 SP2 H:P1*P2 OD. Ho: P1 = P2 H1: P1 * P2 O E. Ho: P1 P2 HP1*P2 OF. Ho: P1 P2 HP1 = P2 Identify the test statistic. ZE (Round to two decimal places as needed.) Identify the P-value. P-value (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? The P-value is the significance level of a = 0.05, so the null hypothesis. There 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 << (P1-P2) < (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. c. Based on the results, does it appear that men and women may have equal success in challenging calls? O A. The confidence interval suggests that there is a significant difference between the success of men and women in challenging calls. It is reasonable to speculate that women have more success. OB. The confidence interval suggests that there is a significant difference between the success of men and women in challenging calls. It is reasonable to speculate that men have more success. C. The confidence interval suggests that there is no significant difference between the success of men and women in challenging calls. OD. There is not enough information to reach a conclusion

Answer 1

Solution Given data X = 423 n = 1398 Pi-xi hi = 423 1398 P = 0.303 X2 = 214 ne = 771 Pa X2 ng 214 Pz = 771 P2= 0.278 X=0.05 Now to state the mull and altermative hypothesis Null hypothesis Ho: Pi=P2 Alternative hypothesis H, : fit pz This is "two-tailed" test

* No find the test statistic Here first to find Pooled Proportion X, 4X2 nithe 423 + 214 1398 +771 P= 637 P- 2169 p= 0.294 We know that The formula of test statistic is given by N VP(-1) (4 + 2) 0.303 -0.278 0.294 (1-0.294) 1398 0.025 Z 0.9940.706) (0.000727 0.00130) 0.025 z = 0.294 (0.706)(0.00202)

Z= 0.00042 0.025 0.0205 1.22 Test statistic, Z=1.22 * Now to find the P-value P-value 2 *[Plz>1.22 = 2x [1-1/2< 1.22) 2 x (1 - 0.8888] - 2 x 0.1112 R-value 0.2224 = 0.222 Conclusion The p-value is greater than the significance level of L=0.05, so failed to reject the hull hypothesis. There is not sufficient evidence to warrant rejection of the claim that women and men have equal success in challenging calls.

Here 1- Confidence interval 2=1-95 loo x=1-0.95 L=0.05 Z. 42=2 0.05 - Z 0.025 Z =1.96 시오 95% confidence interval for pin 12 = [,-) +2012) ni + ng 0.303 (-0.363) 0.3718/1-0.278) +0.303-0.278) † 6.96 + 1398 771 10.303 X 0.697 = 0.025 I 1.96 0.278 X0.722 + 771 1398 =0.025€ 1.96 10.2112 + 1398 0.2007 771 = 0.025 I 1.96 0.000157 0.00026 = 0.025 I 1.96 v 0.00041 = 0.025 – 1960.0202)

(-o. Suggests that there is no significant 95% confidence Interval for Pi-P2 = 0.025 0.0396 -025-0,0396 ,0.025+0.0396 -0.015) 0.065 Because the confidence interval limits includes there does not appear to be a significant difference between the two Proportions There is not enough evidence to warrant have rejection of the and Women claim that men equal Success in Calls. Answer: The confidence interval difference between the success of men in challenging calls. Therefore the "option-c" is the correct answer challenging and Womer