Question

Since an instant replay system for tennis was introduced at a major tournament, men challenged 1408 referee calls, with the result that 417 of the calls were overturned. Women challenged 766 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
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=_____(Round to three decimal places as needed.)

What is the conclusion based on the hypothesis test?

The P-value is (1)_____ the significance level of α=0.05, so (2)_____ the null hypothesis. There (3)_____ 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 (4)_____ 0, there (5) _____ appear to be a significant difference between the two proportions. There (6)_____ evidence to warrant rejection of the claim that men and women have equal success in challenging calls

(1) less than
greater than

(2) fail to reject
reject

(3) is sufficient
is not sufficient

(4) include
do not include

(5) does
does not

(6) is sufficient
is not sufficient

Answer 1

(a) Basic data:

= Sample proportion of men who challenged referee calls successfully = 417/1408 = 0.2962

= Sample proportion of women who challenged referee calls successfully = 214/766 = 0.2794

= Overall Proportion = (417 + 214) / (1408 + 766) = 0.2902

1 - = 0.7098

= 0.05

Since we are testing the claim that men and women have equal successes in challenging calls

The Hypothesis: Option A

H0: p1 = p2

Ha: p1 p2

The Test Statistic:

The p Value: The p value (2 Tail) for Z = 0.82, is; p value = 0.412

The Conclusion: The p value is greater than the significance level of = 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.

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(b) For the 95% Confidence interval

= 0.2962 and 1 - = 0.7038

= 0.2794 and 1 - = 0.7206

The Zcritical (2 tail) for = 0.05, is 1.96

The Confidence Interval is given by (- ) ME, where

(- ) = 0.2962 – 0.2794 = 0.0168

The Lower Limit = 0.0168 - 0.0397 = - 0.0229    -0.023 (Rounding to 3 decimal places)

The Upper Limit = 0.0168 + 0.0397 = 0.0565      0.057 (Rounding to 3 decimal places)

The 95% Confidence Interval is -0.023 < p1 - p2 < 0.057

Because the confidence interval limits includes 0, there does not appear to be a significant difference between the 2 proportions. There is not sufficient evidence to warrant rejection of the claim that women and men have equal success in challenging calls.

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