(Round all intermediate calculations to at least 4 decimal places.) A mortgage s
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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 4.15%? Test the hypothesis at a 1% level of significance. Use Table 2. Financial Institution APR G Squared Financial 4.650% Best Possible Mortgage 4.760 Hersch Financial Group 4.275 Total Mortgages Services 4.780 Wells Fargo 4.670 Quicken Loans 4.440 Amerisave 4.010 SOURCE: MSN Money.com; data retrieved October 1, 2010. Picture Click here for the Excel Data File Use the p-value approach. a-1. Select the null and the alternative hypotheses. H0: µ 4.15; HA: µ < 4.15 H0: µ 4.15; HA: µ > 4.15 H0: = 4.15; HA: 4.15 a-2. Calculate the value of the test statistic. (Round your answer to 2 decimal places.) Test statistic a-3. Approximate the p-value. 0.005 < p-value < 0.010 0.025 < p-value < 0.050 0.010 < p-value < 0.025 p-value < 0.005 p-value Picture 0.05 a-4. What is the conclusion? Reject H0 since the p-value is greater than . Reject H0 since the p-value is smaller than . Do not reject H0 since the p-value is greater than . Do not reject H0 since the p-value is smaller than . Use the critical value approach. b-1. Calculate the critical value. (Round your answer to 3 decimal places.) Critical value b-2. Make a conclusion for the hypothesis test. The mean mortgage rate for the sample exceeds 4.15%. The mean mortgage rate for the sample does not exceed 4.15%. The mean mortgage rate for the population exceeds 4.15%. The mean mortgage rate for the population does not exceed 4.15%.
Explanation / Answer
Solution:
4.650, 4.760, 4.275, 4.780, 4.670, 4.440, 4.010
mean=4.5121 with s=0.286.
you should use the t-dist (since you have a small sample of 7 observations) with 7-1=6 d.f.
from t-table, 1-sided 0.10 critical value is 1.44.
test statistic is (4.5121-4.15)/[0.286/sqrt(7)]= 3.3497
so conclude mean exceeds 4.15%
a-1) H0: µ 4.15; HA: µ < 4.15
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