A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 312 people over the age of​ 55, 78 dream in black and​ white, and among 294 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. 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​: p1p2 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?  b. Test the claim by constructing an appropriate confidence interval. The 98​%

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.