Question

4. A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 322 people over the age of​ 55, 75 dream in black and​ white, and among 281 people under the age of​ 25, 19 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 hypothesis​ test?

A:H 0​: p 1 ≥ 2

H 1​: p 1 ≠ p 2

B.H 0​: p 1= p 2

H 1​: p 1 > p 2

C.H 0​: p 1 ≠ p 2

H 1​: p 1 = p 2

D.H 0​: p 1 = p 2

H 1​: p 1 ≠ p 2

E.H 0​: p 1 = p 2

H 1​: p 1 < p 2

F.H 0​: p 1 ≤p 2

H 1​: p 1 = p 2

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/less than) the significance level of a = 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. b. Test the claim by constructing an appropriate confidence interval.

The 90​% 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/do not include) ​0, it appears that the two proportions are (not equal/equal.) Because the confidence interval limits include (only negative/only positive/positive and 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.

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.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.

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

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