answer the following questions

5. A simple random sample of n = 40 male college students yielded a sample mean weight F = 174.5 lbs. The population standard deviation is known to be o = 12.5 lbs. () (a) Give the best point estimate for the mean weight of male college students. (10) (b) Find the 99% confidence interval for the mean weight of male college students. () (c) Does the interval get smaller or larger if we decrease the confidence level to 95%? Why? (6) 6. (a) Determine the sample size required to estimate the population mean weight of male college students with a margin of error E = 4.0 Ibs and a 99% confidence level. Assume o = 12.5 lbs. Does the required sample size get smaller or larger if (do not need to compute the new sample size): () (b) the margin of error decreases to E = 3.0 lbs? () (c) the confidence level decreases to 95%? 7. A simple random sample of n = 17 car batteries yielded a sample mean life span & = 51.6 months and a sample standard deviation s = 5.4 months. Assume the population of car battery life spans is normally distributed. (10) (a) Find the 95% confidence interval for the mean car battery life span. (4) (b) Explain what the confidence interval means. ()(c) Does the interval get smaller or larger if we increase the sample size n? Why (be specific)?Instructions: Show all work. Show all formulas with proper notation (z, (, s, o, 2, n, N, etc.) and the corresponding numbers inserted. Circle your answers. Round answers to the proper number of decimal places and include the units when appropriate. (10 1. Find the critical value za/2 that corresponds to an 84% confidence interval