Question

Exercise 8-7 Algo In order to estimate the mean 30-year fixed mortgage rate for a home loan in the United States, a random sample of 15 recent loans is taken. The average calculated from this sample is 7.85%. It can be assumed that 30-year fixed mortgage rates are normally distributed with a standard deviation of 0.6%. Compute 90% and 95% confidence intervals for the population mean 30-year fixed mortgage rate. Use Table 1. (Round intermediate calculations to 4 decimal places. Round "z-value" to 3 decimal places and final answers to 2 decimal places. Enter your answers as percentages, not decimals.) Confidence Level 90% 95% Confidence Interval %to %to

Answer 1

Answer

We have

(mean)

(standard deviation)

n = 15 (sample size)

Using the formula

(A) For 90% confidence interval, we have z = 1.645 (using z distribution table for critical value)

setting all the values in the given formula

we get

CI = 7.85 ± 1.645(0.6/V15) = 7.85 ± ( 1.645 * 0.1549)

this gives us

CI 7.85 ± (0.2548) (7.60. 8.10)

So, 90% confidence interval is between 7.60% to 8.10%

(B) For 95% confidence interval, we have z = 1.96 (using z distribution table for critical value)

setting all the values in the given formula

we get

CI 7.85 ± 1.96(0.6/V 15) = 7.85 ± (1.96 * 0.1549)

this gives us

CI 7.85 ± (0.3036) (7.55 8.15)

So, 95% confidence interval is between 7.55% to 8.15%