Question 1130069: 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
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 by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! It is a,
Ho=they are equal
Ha=they are unequal
2-sample proportion, not pooled
(p1-p2)/sqrt ((p1*(1-p1)/n1)+(p2*(1-p2)/n2))
p1=417/1408=0.296, so the first part of the sum above is 0.000148
p2=214/766=0.279, and the second part of the sum is 0.000263
the square root of the whole sum, 0.000411, is 0.0203
p1-p2 is 0.017
z=0.8374
fail to reject Ho, p-value is 0.41, greater than 0.05, so there is insufficient evidence to reject Ho.
The 95% CI has a half interval of z*SE or 1.96*0.0203=0.0398 or 0.040
(-0.023, 0.057), and that contains zero, consistent with failure to reject Ho
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