Hello, could you please help me with these problems, I am having a lot of problems to get the correct results.

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 297 people over the age of 55, 63 dream in black and white, and among 306 people under the age of 25, 17 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? O A. Ho: P1 = P2 O B. Ho: P1 =P2 O C. Ho- P1 = P2 H1: P1 > P2 Hy: P1 # P2 H 1 : P1 = P2 OD. Ho: P1 # P2 O E. HO: P1 = P2 OF. Ho: P1 = P2 Hy : P1 = P2 Hy : P1 = P2 Hy: P1 # P2 Identify the test statistic. Identify the P-value. Z= P-value = (Round to two decimal places as needed.) (Round to three decimal places as needed.) b. Test the claim by constructing an appropriate confidence interval. The 98% confidence interval is =(P1 - P2) P2 H1: P1 = P2 H1: P1 * P2 O D. Ho: P1 = P2 O E. Ho: P1 = P2 OF. Ho: P1 = P2 Hy : P1 = P2 Hy : P1 = P2 Hy : P1 / P 2 Identify the test statistic. Identify the P-value. Z = P-value = (Round to two decimal places as needed.) (Round to three decimal places as needed.) b. Test the claim by constructing an appropriate confidence interval. The appropriate confidence interval is (P1 - P2) = (Round to three decimal places as needed.) c. What do the results suggest about the effectiveness of seat belts? O A. The results suggest that the use of seat belts is associated with lower fatality rates than not using seat belts. O B. The results suggest that the use of seat belts is associated with higher fatality rates than not using seat belts. O C. The results suggest that the use of seat belts is associated with the same fatality rates as not using seat belts. O D. The results are inconclusive.Use the expression in the accompanying discussion of sample size to nd the size of each sample if you want to estimate the difference between proportions of men and women who own smartphones Assume that you want 90% confidence that your error is no more than 0 06 Sample size discussion The sample size needed to estimate the difference between two population proportions to within a margin of error E With a condence level OH 7 u can be found by uSing the followmg expressmn: The sample should include men and women. (Type whole numbers ) Replace n1 and n2 by n in the preceding formula (assuming that both samples have the same Size) and replace each of p1 , q1. p2' and {12 by 0.5 (because their values are not known) SolVing for n results in this expression 2 Zinc/2 2E2 l'l= Rhino viruses typically cause common colds. In a test of the effectiveness of echinacea, 37 of the 43 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 93 of the 106 subjects developed rhinovirus infections. Use a 0.01 significance level to test the claim that echinacea has an effect on rhinovirus infections. Complete parts (a) through (c) below. a. Test the claim using a hypothesis test. Consider the first sample to be the sample of subjects treated with echinacea and the second sample to be the sample of subjects treated with a placebo. What are the null and alternative hypotheses for the hypothesis test? O A. Ho: P1 = P2 O B. Ho: P1 = P2 O C. Ho: P1 # P2 H1: P1 = P2 Hy : P1 # P2 H1 : P1 = P2 O D. Ho: P1 =P2 O E. Ho: P1 = P2 OF. Ho: P1 = P2 H1: P1 # P2 Hy: P1 = P2 Hy : P 1 = P 2 Identify the test statistic. Identify the P-value. Z= P-value = (Round to two decimal places as needed.) (Round to three decimal places as needed.) b. Test the claim by constructing an appropriate confidence interval. The 99% confidence interval is = (P1 - P2) P2 H1: P1 = P2 H1: P1 = P2 Hy : P1 = P2 Identify the test statistic. (Round to two decimal places as needed.) Identify the P-value. (Round to three decimal places as needed.) State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. A. Reject Ho. There is sufficient evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. B. Fail to reject Ho. There is not sufficient evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. C. Reject Ho. There is not sufficient evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. D. Fail to reject Ho. There is sufficient evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. b. Identify the confidence interval limits for the appropriate confidence interval. Let population 1 correspond to the passenger cars and population 2 correspond to the commercial trucks. Let a success be a vehicle that only has a rear license plate. =P1 - P2