A study was conducted to determine the proportion of people who dream in black and white instead of color. Among

324

people over the age of 55,

63

dream in black and white, and among

288

people under the age of 25,

18

dream in black and white. Use a

0.01

significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Complete parts (a) through (c) below.

Question content area bottom

Part 1

a. Test the claim using a hypothesis test.

Consider the first sample to be the sample of people over the age of 55 and the second sample to be the sample of people under the age of 25. What are the null and alternative hypotheses for the hypothesis test?

A.

H0:

p1=p2

H1:

p1

B.

H0:

p1=p2

H1:

p1>p2

C.

H0:

p1p2

H1:

p1p2

D.

H0:

p1=p2

H1:

p1p2

E.

H0:

p1p2

H1:

p1=p2

F.

H0:

p1p2

H1:

p1p2

Part 2

Identify the test statistic.

z=enter your response here

(Round to two decimal places as needed.)

Part 3

Identify the P-value.

P-value=enter your response here

(Round to three decimal places as needed.)Part 4What is the conclusion based on the hypothesis test?The P-value is

less than

greater than

the significance level of

=0.01,

so

fail to reject

reject

the null hypothesis. There is

sufficient

insufficient

evidence to support the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25.Part 5b. Test the claim by constructing an appropriate confidence interval.The

98%

confidence interval is

enter your response here

(Round to three decimal places as needed.)Part 6What is the conclusion based on the confidence interval?Because the confidence interval limits

do not include

include

0, it appears that the two proportions are

equal.

not equal.

Because the confidence interval limits include

positive and negative

only positive

only negative

values, it appears that the proportion of people over 55 who dream in black and white is

greater than

lesser than

not significantly different from

the proportion for those under 25.Part 7c. An explanation for the results is that those over the age of 55 grew up exposed to media that was displayed in black and white. Can these results be used to verify that explanation?

A.

Yes. The results can be used to verify the given explanation because the difference in proportions is practically significant.

B.

Yes. The results can be used to verify the given explanation because the difference in proportions is statistically significant.

C.

No. The results speak to a possible difference between the proportions of people over 55 and under 25 who dream in black and white, but the results cannot be used to verify the cause of such a difference.

D.

No. The results speak to a possible difference between the proportions of people over 55 and under 25 who dream in black and white, but the results are not statistically significant enough to verify the cause of such a difference.