(5)

In a4-week study about the effectiveness of using magnetic insoles to treat plantar heelpain, 54subjects wore magnetic insoles and 42subjects wore nonmagnetic insoles. The results are shown at the right. At =0.09, can you support the claim that there is a difference in the proportion of subjects who feel better between the twogroups? Assume the random samples are independent. Complete parts(a) through(e).

Do you FeelBetter?

A circle graph titled Magnetic Insoles is divided into two sectors with labels and approximate sizes as a percentage of a circle as follows:

Yes, 18, 33.33 percent; No, 36, 66.67 percent.

Magnetic Insoles

Yes18

No36

A circle graph titled Nonmagnetic Insoles is divided into two sectors with labels and approximate sizes as a percentage of a circle as follows: Yes, 21, 50 percent; No, 21, 50 percent.

Nonmagnetic Insoles

Yes21

No21

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(a) Identify the claim and state H0 and Ha.

The claim is"the proportion of subjects who feel better with magnetic insoles is

less than

greater than

the same as

different than

those who feel better with nonmagneticinsoles."

Let

p1 represent the population proportion for the magnetic insoles and

p2 represent the population proportions for the nonmagnetic insoles. State H0 and Ha.

Choose the correct answer below.

A.

H0: p1p2

Ha: p1

B.

H0: p1=p2

Ha: p1p2

C.

H0: p1p2

Ha: p1>p2

D.

H0: p1>p2

Ha:p1p2

E.

H0: p1

Ha: p1p2

F.

H0: p1p2

Ha: p1=p2

(b) Find the criticalvalue(s) and identify the rejectionregion(s).

The criticalvalue(s) is(are) jQuery224029640105421213714_1552871680885???

nothing

Identify the rejectionregion(s). Select the correct choice below and fill in the answerbox(es) within your choice.

A.

z ???

B.

z>

nothing

C.

nothing

nothing

D.

z

nothing

(c) Find the standardized test statistic.

z=

nothing

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

Choose the correct answer below.

FailtorejectH0 because the test statistic is not in the rejection region.

Failtoreject H0 because the test statistic is in the rejection region.

RejectH0 because the test statistic is in the rejection region.

Reject Upper H0 because the test statistic isnot in the rejection region.

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

Choose the correct answer below.

A.

At the 9% significancelevel, there is insufficient evidence to reject the claim.

B.

At the 9% significancelevel, there is insufficient evidence to support the claim.

C.

At the 9% significancelevel, there is sufficient evidence to support the claim.

D.

At the 9% significancelevel, there is sufficient evidence to reject the claim.