Question

In a survey of

one hundred and eight five

females who recently completed high​ school,

eighty percent

were enrolled in college. In a survey of

one hundred and fifty

males who recently completed high​ school,

sixty eight percent

were enrolled in college. At

α=0.07​,

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 H0

and

Upper H Subscript aHa.

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

less than

different than

less than

the same as

or

greater than?

the proportion of male college​ enrollees."Let

p 1

represent the population proportion for female college enrollees and

p2

represent the population proportion for male college enrollees. State

Upper H0

and

Upper H Subscript aHa.

b)

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

The critical​ value(s) is(are)

_____

​(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).

​(c) Find the standardized test statistic.

zequals=_____

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

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

Choose the correct answer below.

a) fail to reject Ho because the test statistic is not in the rejection region

b)reject Ho because the test statistic is not in the rejection region

c) reject Ho because the test statistic is in the rejection region

d) fail to reject Ho because the test statistic is in the rejection region

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

Choose the correct answer below.

a) at the 7% significance level, there is insufficient evidence to support the claim

b) at the 7% significance level, there is sufficient evidence to support the claim

c) at the 7% significance level, there is sufficient evidence to reject the claim

d) at the 7% significance level, there is insufficient evidence to reject the claim

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Answer 1

(a)
Claim: The proportion of female college enrollees is the same as The proportion of female college enrollees.

H0: Null Hypothesis: p1 = p2

Ha:Alternative Hypothesis: p1 p2

(b)

= 0.07

From Table,critical values of Z = 1.81

Rejection region is given by:

Reject H0 if

Z < - 1.81

OR

Z > 1.81

(c)

So,

Q = 1 - P = 0.2537

Test statistic is given by:
Z = (0.80 - 0.68)/0.0479 = 2.51

(d)

Correct option:

(c) reject H0 because the test statistic is in the rejection region

(e) correct option:

(b) At the 7% significance level, there is sufficient evidence to support the claim.