a. b. c. Compute the margin of error at a 95% confidence interval. If the sample

Question

a. b. c. Compute the margin of error at a 95% confidence interval. If the sample mean is 7.58, what is the 95% confidence interval? If the sample mean is 7.58, what is the 99% confidence interval? 8. (3 points) In order to estimate the mean 30-year fixed mortgage rate for a home loan in the United States, a random sample of 28 recent loans is taken. The average calculated from this sample is 5.25%. It can be assumed that 30-year fixed mortgage rates are normally distributed with a standard deviation of 0.50%. a. b. C. Compute the margin of error at a 95% confidence interval. Compute a 95% confidence interval for the population mean 30-year fixed mortgage rate. Compute a 90% confidence interval for the population mean 30-year fixed mortgage rate.

Explanation / Answer

standard deviation=0.5%

sample size=n=28

z(95% confiedance interval)=1.96

margin of error=z*(std dev)/sqrt(n)=1.96*0.5/sqrt(28)=0.1852

ANs b)

Confiedance interval for Population mean will be given as below

((X_-z*std.dev),(X_+z*std dev))=(5.25%-1.96(0.5),5.25%+1.96(0.5)=(4.27%,6.23%)

for 95 % confiedance interval we have z=1.96

((X_-z*std.dev),(X_+z*std dev))=(5.25%-1.64(0.5),5.25%+1.64(0.5)=(4.43%,6.07%)

for 95 % confiedance interval we have z=1.64

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