Question

Since an instant replay system for tennis was introduced at a major​ tournament, men challenged

14421442

referee​ calls, with the result that

417417

of the calls were overturned. Women challenged

768768

referee​ calls, and

219219

of the calls were overturned. Use a

0.050.05

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.

Upper H 0H0​:

p 1p1not equals≠p 2p2

Upper H 1H1​:

p 1p1equals=p 2p2

B.

Upper H 0H0​:

p 1p1greater than or equals≥p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

C.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1less than<p 2p2

D.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

E.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H 1H1​:

p 1p1greater than>p 2p2

F.

Upper H 0H0​:

p 1p1less than or equals≤p 2p2

Upper H 1H1​:

p 1p1not equals≠p 2p2

Identify the test statistic.

zequals=nothing

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

Identify the​ P-value.

​P-valueequals=nothing

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

What is the conclusion based on the hypothesis​ test?

The​ P-value is

▼

greater than

less than

the significance level of

alphaαequals=0.050.05​,

so

▼

reject

fail to reject

the null hypothesis. There

▼

is sufficient

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

▼

do not include

include

​0, there

▼

does not

does

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

▼

is not sufficient

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 women have more success.

B.

The confidence interval suggests that there is no significant difference between the success of men and women in challenging calls.

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.

Click to select your answer(s).

Answer 1

null Hypothesis:    Ho:    p1 =p2

alternate Hypothesis: Ha:   p1 ≠ p2

	College education		No College Education
x1                =	417	x2                =	219
p̂1=x1/n1 =	0.2892	p̂2=x2/n2 =	0.2852
n1                       =	1442	n2                       =	768
estimated prop. diff =p̂1-p̂2    =		0.0040
pooled prop p̂ =(x1+x2)/(n1+n2)=		0.2878
std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =		0.0202
test stat z=(p̂1-p̂2)/Se =		0.20

P value   =

0.8414

The​ P-value is is greater than the significance level of alpha of 0.05 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)

estimated difference in proportion   =p̂1-p̂2   =			0.0040
std error Se =√(p̂1*(1-p̂1)/n1+p̂2*(1-p̂2)/n2) =			0.0202
for 95 % CI value of z=		1.960
margin of error E=z*std error =		0.0396
lower bound=(p̂1-p̂2)-E=		-0.0356
Upper bound=(p̂1-p̂2)+E=		0.0436
from above 95% confidence interval for difference in population proportion =(-0.036 <p1-p2 <0.044)

Because the confidence interval limits include 0.  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.

B.

The confidence interval suggests that there is no significant difference between the success of men and women in challenging calls.