Since an instant replay system for tennis was introduced at a major tournament, men challenged 1386 referee calls, with the result that 429 of the calls were overturned. Women challenged 758 referee calls, and 212 of the calls were overturned. Use a 0.01 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. H0: p1=p2 H1: p1 ≠ p2 B. H0: p1 ≥ p2 H1: p1 ≠ p2 C. H0: p1 ≤ p2 H1: p1 ≠ p2 D. H0: p1 ≠ p2 H1: p1 = p2 E. H0: p1 = p2 H1: p1 > p2 F. H0: p1=p2 H1: p1 < p2 Identify the test statistic. z= ____________ (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 __________ ( A. greater than, B. less than ) the significance level of α=0.01, so _____________ ( A. fail to reject, B. reject ) the null hypothesis. There _____________( A. is not sufficient, B. is 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 ___________ < ( p1−p2 ) < ____________. (Round to three decimal places as needed.) What is the conclusion based on the confidence interval? Because the confidence interval limits ____________( A. include, B. do not include ) 0, there _________________ ( A. does not, B. does ) appear to be a significant difference between the two proportions. There __________ ( A. is not sufficient, B. is sufficient ) 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? 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 men have more success. B. 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. C. The confidence interval suggests that there is no significant difference between the success of men and women in challenging calls. D. There is not enough information to reach a conclusion.
Section 9.1
Question #4
Since an instant replay system for tennis was introduced at a major tournament, men challenged 1386 referee calls, with the result that 429 of the calls were overturned. Women challenged 758 referee calls, and 212 of the calls were overturned. Use a 0.01 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. H0: p1=p2
H1: p1 ≠ p2
B. H0: p1 ≥ p2
H1: p1 ≠ p2
C. H0: p1 ≤ p2
H1: p1 ≠ p2
D. H0: p1 ≠ p2
H1: p1 = p2
E. H0: p1 = p2
H1: p1 > p2
F. H0: p1=p2
H1: p1 < p2
Identify the test statistic.
z= ____________
(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 __________ ( A. greater than, B. less than ) the significance level of α=0.01, so _____________ ( A. fail to reject, B. reject ) the null hypothesis. There _____________( A. is not sufficient, B. is 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 ___________ < ( p1−p2 ) < ____________.
(Round to three decimal places as needed.)
What is the conclusion based on the confidence interval?
Because the confidence interval limits ____________( A. include, B. do not include ) 0, there _________________ ( A. does not, B. does ) appear to be a significant difference between the two proportions. There __________ ( A. is not sufficient, B. is sufficient ) 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?
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 men have more success.
B. 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.
C. The confidence interval suggests that there is no significant difference between the success of men and women in challenging calls.
D. There is not enough information to reach a conclusion.
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