A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 319 people over the age of55, 71 dream in black andwhite, and among 289 people under the age of25, 17 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.

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 hypothesistest?

A.

H0: p1 p 2

H1: p1 p 2

B.

H0: p1 =p 2

H1: p1 >p 2

C.

H0: p1 =p 2

H1: p1 p 2

D.

H0: p1 p 2

H1: p1 =p 2

E.

H0: p1 =p 2

H1: p1

F.

H0: p1 p 2

H1: p1 p 2

Identify the test statistic.

z = ____. (Round to two decimal places asneeded.)

Identify theP-value.

P-value = ____. (Round to three decimal places asneeded.)

What is the conclusion based on the hypothesistest?

TheP-value is

less than

greater than

the significance level of =0.01, so

reject

fail to 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.

b. Test the claim by constructing an appropriate confidence interval.

98% confidence interval is ____ < ( p1 - p2 ) < ____ .

(Round to three decimal places asneeded.)

What is the conclusion based on the confidenceinterval?

Because the confidence interval limits

include

do not include

0, it appears that the two proportions are

not equal.

equal.

Because the confidence interval limits include

only positive

only negative

positive and negative

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

not significantly different from

lesser than

greater than

the proportion for those under 25.

c. 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 thatexplanation?

A.

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

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 andwhite, but the results are not statistically significant enough to verify the cause of such a difference.

D.

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