Question

For the following​ information, determine whether a normal sampling distribution can be​ used, where p is the population​ proportion,

α

is the level of​significance,

p

is the sample​ proportion, and n is the sample size. If it can be​ used, test the claim.​Claim:

p≥0.28​;

α=0.04.

Sample​ statistics:

p=0.20​,

n=140

Let

q=1−p

and let

q=1−p.

A normal sampling distribution

▼

cannot

can

be used​ here, since

▼

npnp

n ModifyingAbove p with caretnp

▼

less than<

greater than or equals≥

5 and

▼

nqnq

n ModifyingAbove q with caretnq

▼

greater than or equals≥

less than<

5.

If a normal sampling distribution can be​ used, identify the hypotheses for testing the claim. Select the correct choice below​ and, if​ necessary, fill in the answer boxes to complete your choice.

A.

H0​:

p<nothing​,

Ha​:

p≥nothing

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

B.

H0​:

p≠nothing​,

Ha​:

p=nothing

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

C.

H0​:

p≤nothing​,

Ha​:

p>nothing

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

D.

H0​:

p=nothing​,

Ha​:

p≠nothing

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

E.

H0​:

p>nothing​,

Ha​:

p≤nothing

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

F.

H0​:

p≥nothing​,

Ha​:

p<nothing

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

G.

A normal sampling distribution cannot be used.

If a normal sampling distribution can be​ used, identify the critical​ value(s) for this test. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

z0=nothing

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

B.

A normal sampling distribution cannot be used.

If a normal sampling distribution can be​ used, identify the rejection​ region(s). Select the correct choice below​ and, if​ necessary, fill in the answer​ box(es) to complete your choice.

A.The rejection region is

z>nothing.

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

B.The rejection region is

z<nothing.

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

C.The rejection regions are

z<nothing

and

z>nothing.

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

D.The rejection region is

nothing<z<nothing.

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

E.

A normal sampling distribution cannot be used.

If a normal sampling distribution can be​ used, identify standardized test statistic z. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

z=nothing

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

B.

A normal sampling distribution cannot be used.

If a normal sampling distribution can be​ used, decide whether to reject or fail to reject the null hypothesis and interpret the decision. Choose the correct answer below.

A.

Reject

the null hypothesis. There

is not

enough evidence to reject the claim.

B.

Fail to reject

the null hypothesis. There

is

enough evidence to reject the claim.

C.

Reject

the null hypothesis. There

is

enough evidence to reject the claim.

D.

Fail to reject

the null hypothesis. There

is not

enough evidence to reject the claim.

E.

A normal sampling distribution cannot be used.

Answer 1

can be used since solution :- A Normal distribution Impp and mq) es Greder than or equal Hoi Þ 0.28 Hai Р L 0.28 I critical = -1.75 Io = Ia = rejection region, Reject Ho z < 1-1.75 7 Ø - 0.200.28 2.11 pll-p) 0.28 x 0.72 140 A Reject the mall hypothesis there is sufficient evidence to reject the claim.