In order to estimate the mean 30-year fixed mortgage rate for a home loan in the

Question

In order to estimate the mean 30-year fixed mortgage rate for a home loan in the United States, a random sample of 26 recent loans is taken. The average calculated from this sample is 7.20%. It can be assumed that 30-year fixed mortgage rates are normally distributed with a standard deviaton of 0.7%. Compute 95% and 99% confidence intervals for the population mean 30-year fixed mortgage rate. Use table 1: http://lectures.mhhe.com/connect/0078020557/Table/table1.jpg

(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.)

Explanation / Answer

here std error =std deviation/(n)1/2  where n=26

=0.1373

and for 99% CI, z=2.576

hence confidence interval =sample mean -/+ z*std error =6.85 ; 7.55

for 95% CI, z=1.96

hence confidence interval =sample mean -/+ z*std error =6.93 ; 7.47

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