The sample standard deviations and sample sizes are given for independent simple random samples from two populations. Use the two-standard-deviations F-test to conduct the required hypothesis test. Two real estate companies, Century 21 and RE/MAX, compete with one another in a local market. The manager of the Century 21 office would like to test the hypotheses that the standard deviation for the number of days that houses listed with RE/MAX is lower than the standard deviation for homes that listed with Century 21. The following data summarizes the sample statistics for the number of days that houses are on the market for both companies. Century 21 RE/MAX Sample standard deviation 29.8 28 Sample size 61 31 Test the hypothesis using = 0.01 a) (5 marks) Find a 95%confidence interval of standard deviation for Century 21. b) (5 marks) Conduct a test of the hypothesis that the variance for Century 21 is more than that for RE/MAX, at 99% confidence level. Show all parts of the hypothesis test, including your hypothesis, your test-statistic calculation and p-value calculations, and your conclusion