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 4.20%? Test the hypothesis at a 10% level of significance. Use Table 2. Financial Institution APR G Squared Financial 4.255% Best Possible Mortgage 4.265 Hersch Financial Group 4.200 Total Mortgages Services 4.540 Wells Fargo 4.175 Quicken Loans 4.225 Amerisave 4.490 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 4.20; HA: µ < 4.20 H0: µ 4.20; HA: µ > 4.20 H0: = 4.20; HA: 4.20 a-2. Calculate the value of the test statistic. (Round your answer to 2 decimal places.) Test statistic a-3. Approximate the p-value. 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 p-value < 0.01 p-value Picture 0.1 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 4.20%. The mean mortgage rate for the sample does not exceed 4.20%. The mean mortgage rate for the population exceeds 4.20%. The mean mortgage rate for the population does not exceed 4.20%.

Explanation / Answer

The statistical software output for this problem is:

One sample T hypothesis test:
: Mean of variable
H0 : = 4.2
HA : > 4.2

Hypothesis test results:

Hence,

H0: µ 4.20; HA: µ > 4.20

Test statistic = 1.94

0.050 < p-value < 0.100

Reject H0 since the p-value is smaller than .

Critical value = 1.440

The mean mortgage rate for the population exceeds 4.20%.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.