Question

In order to estimate the mean 30-year fixed mortgage rate for a home loan in the United States, a random sample of 24 recent loans is taken. The average calculated from this sample is 6.80%. It can be assumed that 30-year fixed mortgage rates are normally distributed with a population standard deviation of 0.5%. Compute 95% and 99% confidence intervals for the population mean 30-year fixed mortgage rate. (Round intermediate calculations to at least 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 Confidence to Interval

95%.   ________% to  _______%

99%. ________% to  _______%

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 6.80%

Population standard deviation =    = 0.5%

Sample size = n = 24

a) At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.960

Margin of error = E = Z/2 * ( /n)

= 1.960 * ( 0.5% /  24 )

= 0.20%

At 95% confidence interval estimate of the population mean is,

  ± E

6.80% ± 0.20%

( 6.60% to 7.00% )  

b) At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005 = 2.576

Margin of error = E = Z/2 * ( /n)

= 2.576 * ( 0.5% /  24 )

= 0.26%

At 99% confidence interval estimate of the population mean is,

  ± E

6.80% ± 0.26%

( 6.54% to  7.06% )