In order to estimate the mean 30year fixed mortgage rate for

In order to estimate the mean 30-year fixed mortgage rate for a home loan In the United States, a random sample of 13 recent loans s taken. The average calculated from this sample s 6.30%. It can be assumed that 30-year fixed mortgage rates are normally distributed with a standard deviation of 0.50%. Compute a 90% and a 95% confidence interval for the population mean 30-year fixed mortgage rate. Use Table 1. (Round your intermediate calculations to 4 decimal places, z value and final answers to 2 decimal places.)

Solution

1) 90%

Mean = 6.30%

SD=0.5%

z for 90% = 1.65

Standard Error = (z*SD)/sqrt(n)

= ( 1.65 * 0.5) / sqrt(13)

= 0.2288

Therefore,

Confidence Interval :

=((6.3 - 0.2288)% , (6.3+0.2288))

=(6.0712,6.5288)

= ( 6.07 , 6.53 ) Answer

2) 95%

Mean = 6.30%

SD=0.5%

z for 90% = 1.96

Standard Error = (z*SD)/sqrt(n)

= ( 1.96 * 0.5) / sqrt(13)

= 0.2718

Therefore,

Confidence Interval :

=((6.3 - 0.2718)% , (6.3+0.2718))

=(6.0282,6.5718)

= ( 6.03 , 6.57 ) Answer