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 22 recent loans is taken. The average calculated from this sample is 7.60%. It can be assumed that 30-year fixed mortgage rates are normally distributed with a standard deviation of 0.4%. Compute 95% and 99% 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 Confidence Interval 95% % to % 99% % to %

Explanation / Answer

= 7.60 = 0.4 n = 22

Let (a,b) be the 95% confidence interval.

z = 1.96

a = - z / n

= 7.60 - 1.96*0.4 / 22

= 7.60 - 0.1671

= 7.4329.

b = + z / n

= 7.60 + 1.96*0.4 / 22

= 7.60 + 0.1671

= 7.7671.

The 95% confidence interval is 7.4329% to 7.7671%.

Let (a,b) be the 95% confidence interval.

z = 2.576

a = - z / n

= 7.60 - 2.576*0.4 / 22

= 7.60 - 0.2197

= 7.3803.

b = + z / n

= 7.60 + 2.576*0.4 / 22

= 7.60 + 0.2197

= 7.8197.

The 95% confidence interval is 7.3803% to 7.8197%.

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