value 12.00 points Exercise 8-7 Algo In order to estimate the mean 30-year fixed

Question

value 12.00 points Exercise 8-7 Algo In order to estimate the mean 30-year fixed motgage rate for a sample of 25 recent loans is taken The averagecalculated fromthis sample is 6 20% It can be assumed that 30-year fixed mortgage rates are normally distributed with a standard deviation of 0 3% Compute 90% and 95% confidence intervals for the population mean 30-year fixed mortgage rate Use Tablet (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.) horne loan in the United States, a random Confidence Level 90% 95% Confidence Interval %to % to Search the web and Windows Lenovo

Explanation / Answer

Solution:

Sample size = n = 25

Sample mean = M = 6.2

Sample standard deviation = s = 0.3

(a) 90% CI for mean:

CL = 0.90 then Z = 1.64

Now we calculate standard error

sM = (0.32/25) = 0.06

Formula of CI for mean is
= M ± Z(sM)
= 6.2 ± 1.64*0.06
= 6.2 ± 0.099

Hence 90% CI for population mean is (6.101%, 6.299%)

(b) 95% CI for mean:

CL = 0.95 then Z = 1.96

Now we calculate standard error

sM = (0.32/25) = 0.06

Formula of CI for mean is
= M ± Z(sM)

= 6.2 ± 1.96*0.06
= 6.2 ± 0.118

Hence 99% CI for population mean is (6.082%, 6.318%)

Done

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