Question

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 299 people over the age of 55, 61dream in black and white, and among

287 people under the age of 25, 10 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 hypothesis test?

A. H₀: P₁ ≥ P2, H1: P₁ ≠ P₂

B. H₀: P₁ ≤ P2, H1: P₁ ≠ P₂

C. H₀: P₁ ≠ P2, H1: P₁ ≠ P₂

D. H₀: P₁ = P2, H1: P₁ > P₂

E. H₀: P₁ = P2, H1: P₁ < P₂

F. H₀: P₁ = P2, H1: P₁ ≠ P₂

Identify the test statistic.

z =

(Round to two decimal places as needed.)

Identify the P-value.

P-value =

(Round to three decimal places as needed.)

What is the conclusion based on the hypothesis test?

The P-value is (greater than or less than) the significance level of a = 0.01 , so (reject or fail to reject) the null hypothesis. There is (insufficient or 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.

The 98 % confidence interval is ____ < (P₁ - P₂ ) < ____.

(Round to three decimal places as needed.)

What is the conclusion based on the confidence interval?

Because the confidence interval limits (include or do not include) 0, it appears that the two proportions are (not equal or equal). Because the confidence interval limits include

( positive and negative or only positive or only negative) values, it appears that the proportion of people over 55 who dream in black and white is (lesser than or not significantly different from

or 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 that explanation?

A. Yes. The results can be used to verify the given explanation because the difference in proportions is practically 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 cannot be used to verify the cause of such a difference.

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

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.

Answer 1