A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 314 people over the age of 55, 77 dream in blackand white, and among 283 people under the age of 25, 18 dream in black and white. Use a 0.01 significance level to test the claim that the proportion of people over 55who 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 andalternative hypotheses for the hypothesis test?O A. Ho: P1 = P2H1: P1 P2Identify the test statistic.(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 isthe significance level of a = 0.01, sothe null hypothesis. There isevidence to support the claim that the The P-value isthe significance level of a = 0.01, sothe null hypothesis. There isevidence to support the claim that theproportion 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.(P1 - P2) <.(Round to three decimal places as needed.)The 98% confidence interval is<What is the conclusion based on the confidence interval?Because the confidence interval limits0, it appears that the two proportions areBecause the confidence interval limits includevalues, it appears that the proportion of people over 55 who dream in black and white isthe proportion forthose 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 verifythat explanation?O 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 cannotbe used to verify the cause of such a difference.O 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 notstatistically significant enough to verify the cause of such a difference.

Name: A study was conducted to determine the proportion of people who dream
Uploaded: 2024-03-20T07:07:00.000Z
Channel: Bartleby
Description: A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 314 people over the age of 55, 77 dream in blackand white, and among 283 people under the age of 25, 18 dream in black and white. Use a

Given Information: Over the age 55: Sample size (n1) = 314 x1 = 77 Under the age 25: Sample size…

Math

Statistics

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 314 people over the age of 55, 77 dream in and white, and among 283 people under the age of 25, 18 dream in black and white. Use a 0.01 significance level to test the claim that the proportion of people c 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 nul alternative hypotheses for the hypothesis test? O A. Ho: P1 = P2 O B. Ho: P1 = P2 H1: P1 #P2 O C. Ho: P1 SP2 H1: P1 #P2 H1:P1 P2 H1: P1 #P2 Identify the test statistic. z= (Round to two decimal places as needed.) Identify the P-value. P-value =