Question

In a survey of

184184

females who recently completed high​ school,

7575​%

were enrolled in college. In a survey of

175175

males who recently completed high​ school,

7272​%

were enrolled in college. At

alpha equals 0.06α=0.06​,

can you reject the claim that there is no difference in the proportion of college enrollees between the two​ groups? Assume the random samples are independent. Complete parts​ (a) through​ (e).

​(a) Identify the claim and state

Upper H 0H0

and

Upper H Subscript aHa.

The claim is​ "the proportion of female college enrollees is

▼

less than

the same as

greater than

different than

the proportion of male college​ enrollees."Let

p 1p1

represent the population proportion for female college enrollees and

p 2p2

represent the population proportion for male college enrollees. State

Upper H 0H0

and

Upper H Subscript aHa.

Choose the correct answer below.

A.

Upper H 0H0​:

p 1p1less than or equals≤p 2p2

Upper H Subscript aHa​:

p 1p1greater than>p 2p2

B.

Upper H 0H0​:

p 1p1not equals≠p 2p2

Upper H Subscript aHa​:

p 1p1equals=p 2p2

C.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H Subscript aHa​:

p 1p1not equals≠p 2p2

D.

Upper H 0H0​:

p 1p1greater than or equals≥p 2p2

Upper H Subscript aHa​:

p 1p1less than<p 2p2

E.

Upper H 0H0​:

p 1p1greater than>p 2p2

Upper H Subscript aHa​:

p 1p1less than or equals≤p 2p2

F.

Upper H 0H0​:

p 1p1less than<p 2p2

Upper H Subscript aHa​:

p 1p1greater than or equals≥p 2

(b) Find the critical​ value(s) and identify the rejection​ region(s).

The critical​ value(s) is(are)

nothing.

​(Use a comma to separate answers as needed. Type an integer or a decimal. Round to two decimal places as​ needed.)

Identify the rejection​ region(s). Select the correct choice below and fill in the answer​ box(es) within your choice. ​(Round to two decimal places as​ needed.)

A.

nothingless than<zless than<nothing

B.

zgreater than>nothing

C.

zless than<nothing

and

zgreater than>nothing

D.

zless than<nothing

​(c) Find the standardized test statistic.

zequals=nothing

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

​(d) Decide whether to reject or fail to reject the null hypothesis.

Choose the correct answer below.

Fail to rejectFail to reject

Upper H 0H0

because the test statistic

is notis not

in the rejection region.

Fail to rejectFail to reject

Upper H 0H0

because the test statistic

isis

in the rejection region.

RejectReject

Upper H 0H0

because the test statistic

is notis not

in the rejection region.

RejectReject

Upper H 0H0

because the test statistic

isis

in the rejection region.

​(e) Interpret the decision in the context of the original claim.

Choose the correct answer below.

A.At the

66​%

significance​ level, there is

sufficientsufficient

evidence to support the claim.

B.At the

66​%

significance​ level, there is

sufficientsufficient

evidence to reject the claim.

C.At the

66​%

significance​ level, there is

insufficientinsufficient

evidence to support the claim.

D.At the

66​%

significance​ level, there is

insufficientinsufficient

evidence to reject the claim.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 ≠ p2

b)

This is two tailed test, for α = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96

c)

p1cap = X1/N1 = 138/184 = 0.75
p1cap = X2/N2 = 126/175 = 0.72
pcap = (X1 + X2)/(N1 + N2) = (138+126)/(184+175) = 0.7354

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.75-0.72)/sqrt(0.7354*(1-0.7354)*(1/184 + 1/175))
z = 0.64

d)

Fail to reject H0 because the test statistic is not in the rejection region.

e)

.At the

66​%

significance​ level, there is

insufficientinsufficient

evidence to support the claim.