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 4.35%? Test the hypothesis at a 5% level of significance. Use Table 2.

Calculate the value of the test statistic. (Round intermediate calculations to 4 decimal places. 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 4.35%? Test the hypothesis at a 5% level of significance. Use Table 2.

Explanation / Answer

a-1.

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   4.35  
Ha:    u   >   4.35   [ANSWER, C]

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a-2.

Getting the test statistic, as              
              
X = sample mean =    4.497857143          
uo = hypothesized mean =    4.35          
n = sample size =    7          
s = standard deviation =    0.28748706          
              
Thus, t = (X - uo) * sqrt(n) / s =    1.360733349   [ANSWER]

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a-3.
              
As we can see, this is a    right   tailed test.                      
df = n - 1 =    6          

Hence, by table,

OPTION B: 0.100 < p < 0.200 [ANSWER]

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a-4.

As P > 0.05,

OPTION B: Do not reject H0 since the p-value is greater than . [ANSWER, B]

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b-1.

As it is 0.05 level, right tailed, df = 6,

tcrit = 1.943   [ANSWER]

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b-2.

As t < 1.943,

OPTION C: c) The mean mortgage rate for the population does not exceed 4.35% [ANSWER, C]

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