Question

Since an instant replay system for tennis was introduced at a major​ tournament, men challenged 1441 referee​ calls, with the result that 422 of the calls were overturned. Women challenged 758 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?

Identify the test statistic.

Identify the​ P-value.

What is the conclusion based on the hypothesis​ test?

The​ P-value is

(less than or greater than)

the significance level of

alpha =0.05​, so

(reject OR fail to reject) the null hypothesis. There

(is sufficient OR 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

9595​%

confidence interval is

nothingless than<left parenthesis p 1 minus p 2 right parenthesisp1−p2less than<nothing.

​(Round to three decimal places as​ needed.)

What is the conclusion based on the confidence​ interval?

Because the confidence interval limits

(include OR do not include)

​0, there

(does not OR does)

appear to be a significant difference between the two proportions. There

(is not sufficient OR 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 no significant difference between the success of men and women in challenging calls.

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 a significant difference between the success of men and women in challenging calls. It is reasonable to speculate that men have more success.

D.

There is not enough information to reach a conclusion.

Answer 1

using excel>addin>phstat<two sample test >z test for difference

we have

Z Test for Differences in Two Proportions
Data		Confidence Interval Estimate
Hypothesized Difference	0		of the Difference Between Two Proportions
Level of Significance	0.05
Group 1			Data
Number of Items of Interest	422		Confidence Level	95%
Sample Size	1441
Group 2			Intermediate Calculations
Number of Items of Interest	216		Z Value	-1.9600
Sample Size	758		Std. Error of the Diff. between two Proportions	0.0203
			Interval Half Width	0.0398
Intermediate Calculations
Group 1 Proportion	0.292852186		Confidence Interval
Group 2 Proportion	0.284960422		Interval Lower Limit	-0.0319
Difference in Two Proportions	0.007891764		Interval Upper Limit	0.0477
Average Proportion	0.2901
Z Test Statistic	0.3876
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.6983
Do not reject the null hypothesis

a. the null and alternative hypotheses for the hypothesis​ test

Ho:p1=p2

HA:p1 p2

the test statistic is 0.3876

the​ P-value is 0.3876

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 -0.0319<p 1 - p 2<0.048

What is the conclusion based on the confidence​ interval?

Because the confidence interval limits include ​0, there does not appear to be a significant difference between the two proportions. There is not 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 no significant difference between the success of men and women in challenging calls.