A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 303 people over the age of55, 73 dream in black andwhite, and among 290 people under the age of25, 13 dream in black and white. Use a 0.05 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.

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=p2

H1: p1p2

B.

H0: p1p2

H1: p1=p2

C.

H0: p1=p2

H1: p1

D.

H0: p1p2

H1: p1p2

E.

H0: p1p2

H1: p1p2

F.

H0: p1=p2

H1: p1>p2

Identify the test statistic.

z=

nothing

(Round to two decimal places asneeded.)

Identify theP-value.

P-value=

nothing

(Round to three decimal places asneeded.)

What is the conclusion based on the hypothesistest?

TheP-value is

greater than

less than

the significance level of =0.05, so

fail to reject

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.

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