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 26 recent loans is taken. The average calculated from this sample is 6.60%. It can be assumed that 30-year fixed mortgage rates are normally distributed with a standard deviation of 0.5%. Compute 90% and 95% confidence intervals for the population mean 30-year fixed mortgage rate. Use Table 1. (Round intermediate calculations to 4 decimal places, \"z\" value and final answers to 2 decimal places. Enter your answers as percentages, not decimals.)

Solution

For 90% confidence:

Note that              
              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.05          
X = sample mean =    6.6          
z(alpha/2) = critical z for the confidence interval =    1.64          
s = sample standard deviation =    0.5          
n = sample size =    26          
              
Thus,              
              
Lower bound =    6.439184769          
Upper bound =    6.760815231          
              
Thus, the confidence interval is              
              
(   6.44   ,   6.76   ) [answer]

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For 95% confidence:

Note that              
              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    6.6          
z(alpha/2) = critical z for the confidence interval =    1.96          
s = sample standard deviation =    0.5          
n = sample size =    26          
              
Thus,              
              
Lower bound =    6.407806188          
Upper bound =    6.792193812          
              
Thus, the confidence interval is              
              
(   6.41   ,   6.79   ) [ANSWER]