Question

An education researcher claims that

58​%

of college students work​ year-round. In a random sample of

300

college​ students,

174

say they work​ year-round. At

α=0.10​,

is there enough evidence to reject the​ researcher's claim? Complete parts​ (a) through​ (e) below.

a) Identify the claim and state

H0

and

Ha.

Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice.

​(Type an integer or a decimal. Do not​ round.)

A.The percentage of college students who work​ year-round is not

nothing​%.

B.At least

nothing​%

of college students work​ year-round.

C.At most

nothing​%

of college students work​ year-round.

D.

nothing​%

of college students work​ year-round.

Let p be the population proportion of​ successes, where a success is a college student who works​ year-round. State

H0

and

Ha.

Select the correct choice below and fill in the answer boxes to complete your choice.

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

A.

H0​:

p<nothing

Ha​:

p≥nothing

B.

H0​:

p=nothing

Ha​:

p≠nothing

C.

H0​:

p≥nothing

Ha​:

p<nothing

D.

H0​:

p≤nothing

Ha​:

p>nothing

E.

H0​:

p>nothing

Ha​:

p≤nothing

F.

H0​:

p≠nothing

Ha​:

p=nothing

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

Identify the critical​ value(s) for this test.

z0=nothing

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

Identify the rejection​ region(s). Select the correct choice below and fill in the answer​ box(es) to complete your choice.

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

A.The rejection region is

z<nothing.

B.The rejection region is

nothing<z<nothing.

C.The rejection regions are

z<nothing

and

z>nothing.

D.The rejection region is

z>nothing.

​(c) Find the standardized test statistic z.

z=nothing

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

​(d) Decide whether to reject or fail to reject the null hypothesis and​ (e) interpret the decision in the context of the original claim.

▼

Fail to reject

Reject

the null hypothesis. There

▼

is

is not

enough evidence to

▼

reject

support

the​ researcher's claim.

Answer 1