Question

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

1389

referee​ calls, with the result that

428

of the calls were overturned. Women challenged

756

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.

Upper H 0

​:

p 1

equalsp 2

Upper H 1

​:

p 1

greater thanp 2

B.

Upper H 0

​:

p 1

not equalsp 2

Upper H 1

​:

p 1

equalsp 2

C.

Upper H 0

​:

p 1

equalsp 2

Upper H 1

​:

p 1

not equalsp 2

D.

Upper H 0

​:

p 1

less than or equalsp 2

Upper H 1

​:

p 1

not equalsp 2

E.

Upper H 0

​:

p 1

greater than or equalsp 2

Upper H 1

​:

p 1

not equalsp 2

F.

Upper H 0

​:

p 1

equalsp 2

Upper H 1

​:

p 1

less thanp 2

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

▼

less than

greater than

the significance level of

alpha

equals0.01

​,

so

▼

fail to reject

reject

the null hypothesis. There

▼

is not sufficient

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

99

​%

confidence interval is

nothing

less thanleft parenthesis p 1 minus p 2 right parenthesisless thannothing

.

​(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

does not

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

▼

is sufficient

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

Click to select your answer(s).

Answer 1