A study was conducted to determine the proportion of people who dream in black a

Question

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 304 304 people over the age of 55, 72 72 dream in black and white, and among 311 311 people under the age of 25, 15 15 dream in black and white. Use a 0.05 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. Upper H 0 H0: p 1 p1 equals = p 2 p2 Upper H 1 H1: p 1 p1 less than < p 2 p2 B. Upper H 0 H0: p 1 p1 equals = p 2 p2 Upper H 1 H1: p 1 p1 not equals p 2 p2 C. Upper H 0 H0: p 1 p1 equals = p 2 p2 Upper H 1 H1: p 1 p1 greater than > p 2 p2 D. Upper H 0 H0: p 1 p1 greater than or equals p 2 p2 Upper H 1 H1: p 1 p1 not equals p 2 p2 E. Upper H 0 H0: p 1 p1 less than or equals p 2 p2 Upper H 1 H1: p 1 p1 not equals p 2 p2 F. Upper H 0 H0: p 1 p1 not equals p 2 p2 Upper H 1 H1: p 1 p1 equals = p 2 p2 Identify the test statistic. z equals = (Round to two decimal places as needed.) Identify the P-value. P-value equals = (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? The P-value is the significance level of alpha equals = 0.05 0.05, so the null hypothesis. There is 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 90 90% confidence interval is less than < left parenthesis p 1 minus p 2 right parenthesis p1p2 less than < . (Round to three decimal places as needed.) What is the conclusion based on the confidence interval? Because the confidence interval limits 0, it appears that the two proportions are Because the confidence interval limits include values, it appears that the proportion of people over 55 who dream in black and white is 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 statistically 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 are not statistically significant enough 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. Click to select your answer(s).

Explanation / Answer

The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 > 0

Hypothesis test results:

90% confidence interval results:

Hence,

Hypotheses:

Ho: p1 = p2

H1: p1 > p2

z = 6.71

P - value = 0.000

P - value is less than significance level, reject the null hypothesis.

90% confidence interval: 0.144 < p1 - p2 < 0.233

Because the confidence interval limits include only positive values, it appears that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25.

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. Option A

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