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Part 1

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

305

people over the age of 55,

68

dream in black and white, and among

294

people under the age of 25,

15

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.

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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 0:

p1not equalsp 2

Upper H1:

p1equals=p2

B.

Upper H 0H:

p 1less than or equalsp 2

Upper H1:

p 1not equalsp 2

C.

Upper H 0:

p 1equals=p 2

Upper H 1:

p 1greater than>p 2

D.

Upper H 0:

p 1equals=p 2

Upper H 1:

p 1not equalsp 2

E.

Upper H 0:

p 1equals=p 2

Upper H 1:

p 1less than

F.

Upper H 0:

p 1greater than or equalsp 2

Upper H 1:

p 1not equalsp 2

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=0.01,

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

98%

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

do not include

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

greater than

not significantly different from

lesser than

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.

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.

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.

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

What are the null and alternative hypotheses for the hypothesis test?z(Round to two decimal places as needed.)P-value(Round to three decimal places as needed.)The P-value is0.01the significance level of 0.01, sothe null hypothesis.There isevidence 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.The 98% confidence interval isleft parenthesis p 1 minus p 2 right parenthesisleft parenthesis p 1 minus p 2 right parenthesis(Round to three decimal places as needed.)Because the confidence interval limits0, it appears that the two proportions are0, it appears that the two proportions areBecause the confidence interval limits includeBecause the confidence interval limits includevalues, it appears that the proportion of people over 55 who dream in black and white isvalues, it appears that the proportion of people over 55 who dream in black and white isthe proportion for those under 25.Can these results be used to verify that explanation?