A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 318 people over the age of​ 55, 72 dream in black and​ white, and among 286 people under the age of​ 25, 13 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. Question content area bottom 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​: p 1greater than or equalsp 2 Upper H 1​: p 1not equalsp 2 B. Upper H 0​: p 1less than or equalsp 2 Upper H 1​: p 1not equalsp 2 C. Upper H 0​: p 1equalsp 2 Upper H 1​: p 1greater thanp 2 Your answer is correct.D. Upper H 0​: p 1equalsp 2 Upper H 1​: p 1less thanp 2 E. Upper H 0​: p 1equalsp 2 Upper H 1​: p 1not equalsp 2 F. Upper H 0​: p 1not equalsp 2 Upper H 1​: p 1equalsp 2 Part 2 Identify the test statistic. zequals    6.39 ​(Round to two decimal places as​ needed.) Part 3 Identify the​ P-value. ​P-valueequals    0.000 ​(Round to three decimal places as​ needed.) Part 4 What is the conclusion based on the hypothesis​ test? The​ P-value is less than the significance level of alphaequals0.01​, so reject the null hypothesis. There is 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    0.119less thanleft parenthesis p 1 minus p 2 right parenthesisless than    0.243. ​(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 ​0, it appears that the two proportions are not equal. 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. 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. Yes. The results can be used to verify the given explanation because the difference in proportions is practically 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 cannot be used to verify the cause of such a difference.