Question

olo Mortgage rates: Following are interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia, on June 20, 2013. Assume that the population is approximately normal. 4.286 4.325 4.134 4.581 4.908 4.429 4.689 3.319 4.84 4.568 4.847 4.996 Send data to Excel Part 1 of 3 (a) Find the sample standard deviation s. Round the answer to at least four decimal places. The sample standard deviation s is 0.4578 Part: 1/3 Part 2 of 3 (b) Construct an 80% confidence interval for the population standard deviation o. Round the answers to at least two decimal places. An 80% confidence interval for the population standard deviation is <o< 0.

2 Based on the confidence that the population standard deviation of mortgage rates is greater than 0.7

Answer 1

a) The sample standard deviation is s = 0.4578

b)

c) Since lower bound and upper bound < 0.7, so we can conclude that the population standard deviation of mortgage rates is not significantly greater than 0.7.

Let s? denotes the sample variance, s denotes the sample standard deviation and n denotes the sample size. Here, sa = 0.209552, s = 0.4578, n = 12 The lower critical value is xłower-critical X0.9,11 = 5.577785 5.578 The upper critical value is Xupper-critical = X0.1,11 = 17.275009 ~ 17.275 a 80 percent confidence interval of population variance o2 is (n-1) * 82 (n − 1) * 82 1-0.80 n-1 1-0.80 ,n-1 2 2 2 X1-0,20,11 (12 – 1) * 0.209552 (12-1) * 0.209552 X 6,20,11 (12 - 1) * 0.209552 (12 – 1) * 0.209552 17.275009 5.577785 (0.133434, 0.413259) Now, a 80 percent confidence interval of population standard deviation o is = (10.133434, 0.413259) = (0.365286, 0.642852) ~ (0.37,0.64)