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

289289

people over the age of 55,

6363

dream in black and white, and among

284284

people under the age of 25,

1010

dream in black and white. Use a

0.050.05

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.

Upper H 0H0:

p 1p1less than or equalsp 2p2

Upper H 1H1:

p 1p1not equalsp 2p2

B.

Upper H 0H0:

p 1p1equals=p 2p2

Upper H 1H1:

p 1p1less than

C.

Upper H 0H0:

p 1p1greater than or equalsp 2p2

Upper H 1H1:

p 1p1not equalsp 2p2

D.

Upper H 0H0:

p 1p1equals=p 2p2

Upper H 1H1:

p 1p1not equalsp 2p2

E.

Upper H 0H0:

p 1p1equals=p 2p2

Upper H 1H1:

p 1p1greater than>p 2p2

F.

Upper H 0H0:

p 1p1not equalsp 2p2

Upper H 1H1:

p 1p1equals=p 2p2

Part 2

Identify the test statistic.

zequals=enter your response here

(Round to two decimal places as needed.)

Part 3

Identify the P-value.

P-valueequals=enter your response here

(Round to three decimal places as needed.)

Part 4

What is the conclusion based on the hypothesis test?

The P-value is

greater than

less than

the significance level of

alphaequals=0.050.05,

so

reject

fail to reject

the null hypothesis. There is

insufficient

sufficient

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 5

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

The

9090%

confidence interval is

enter your response hereless than

(Round to three decimal places as needed.)

Part 6

What is the conclusion based on the confidence interval?

Because the confidence interval limits

include

do not include

0, it appears that the two proportions are

equal.

not equal.

Because the confidence interval limits include

only positive

positive and negative

only negative

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

lesser than

greater than

not significantly different from

the proportion for those under 25.

Part 7

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 that explanation?

A.

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

B.

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