Question

Following are interest rates (annual percentage rates) for a 30-year-fixed-rate mortgage from a sample of lenders in a certain city. It is reasonable to assume that the population is approximately normal. 4.327, 4.461, 4.547, 4.662 , 4.365, 4.526 , 4.842 Find the upper bound of the 99% confidence interval for the mean rate.

Answer 1

Hey There!:

Sample Mean = 4.4823

SD = 0.1859

Sample Size (n) = 7

Standard Error (SE) = SD/root(n) = 0.0703

alpha (a) = 1-0.99 = 0.01

t(a/2, n-1 ) =  3.7074

Margin of Error (ME) =  t(a/2,n-1)x SE = 0.2606

99% confidence interval is given by:

Sample Mean +/- (Margin of Error)

4.4823 +/- 0.2606 = (4.222 , 4.743)

Hope this helps!