A mortgage specialist would like to analyze the average mortgage rates for Atlan

Question

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. Use Table 2.

Calculate the value of the test statistic. (Round your answer to 2 decimal places.)

Calculate the critical value. (Round your answer to 3 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. Use Table 2.

Explanation / Answer

Based on the given data , the mean apr and standard apr must be calculated first

so mean = 4.470

and SD = 0.3019

now the t stat is given as

t = (mean1 - mean2) /sd/sqrt(n) = (4.47-4.10)/(0.3019/sqrt(7)) = 3.24 (test statistic)

The hypothesis is

H0: µ 4.10; HA: µ > 4.10 , and it is one tail directional test as we are interested in the "exceed"

the critical value can be found using the t table for df = n-1 = 7-1 = 6 and alpha = 0.05

the critcal value is 1.94

as the t stat is greater than the t critical value , hence we fail to reject the null hypothesis and conclude that

The mean mortgage rate for the sample does not exceed 4.10%.

Please note that we can aswer only 4 subparts of the question , at a time , as per the answering guidelines

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