answer all questions with explanation

6. A school wants to estimate the mean SAT math score for their graduating seniors. The seniors estimate the average score for the seniors. The school has 56 seniors in track A, 80 seniors in track B, and 64 students in track C. The costs of sampling are equal for all strata, but the variances are 1600, 2500, and 900 for A, B, and C, respectively. a. Find the sample size needed to estimate the average score with a bound of 5 points on the error of estimation using Neyman allocation. (You do not need to provide the sample size for each stratum just provide the overall sample size, n.) b. Suppose there are 66 seniors in track A, 90 in track B, and 74 in track C, with variances of 1600, 2500, and 900 for A, B, and C, respectively. Will the sample size increase or decrease, compared to part (a)? Explain your answer. (You do not actually have to calculate the sample size.) c. Suppose there are 56 seniors in track A, 80 in track B, and 64 in track C, with variances of 1400, 2300, and 700 for A, B, and C, respectively. Will the sample size increase or decrease, compared to part (a)? Explain your answer. (You do not actually have to calculate the sample size.)