(Round all intermediate calculations to at least 4 decimal places.) A mortgage s

Question

(Round all intermediate calculations to at least 4 decimal places.)

A mortgage specialist would like to analyze the average mortgage rates for Atlanta, Georgia. He studies the following sample APR quotes. These are the annual percentage rates (APR) for 30-year fixed loans. If he is willing to assume that these rates are randomly drawn from a normally distributed population, can he conclude that the mean mortgage rate for the population exceeds 4.10%? Test the hypothesis at a 10% level of significance.

Calculate the critical value. (Round your answer to 3 decimal places.)

(Round all intermediate calculations to at least 4 decimal places.)

A mortgage specialist would like to analyze the average mortgage rates for Atlanta, Georgia. He studies the following sample APR quotes. These are the annual percentage rates (APR) for 30-year fixed loans. If he is willing to assume that these rates are randomly drawn from a normally distributed population, can he conclude that the mean mortgage rate for the population exceeds 4.10%? Test the hypothesis at a 10% level of significance.

Explanation / Answer

H0 : MMR 4.10%

Ha : MMR > 4.10%

Here in the given sample,

sample mean MMR, xMMR = 4.47%

sample standard deviation s = 0.3028%

Here , n = 7

Test statistic

t = (x - MMR)/ (s/ sqrt(n) = (4.47 - 4.10)/ [0.302848 /sqrt(7)] = 0.37/ 0.114466 = 3.2324

Here dF = 7 -1 = 6 and alpha = 0.10

tcritical = 1.440

Here t > tcritical so the mean mortgage rate for the population exceeds 4.10%. Option C is correct.

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