Starting in 2008 an increasing number of people found themse

Starting in 2008 an increasing number of people found themselves facing mortgages that were worth more than the value of their homes. A fund manager who had invested in debt obligation involving grouped mortgages was interested in determining the group most likely to default on their mortgage. He speculates that older people are less likely to default on their mortgage and thinks the average of those who do is less than 55 years to test this a random sample of 30 who had defaulted was selected. the sample data below reflect the ages of sampled individuals.

41 49 56 30 33 55 70 63 39 69 78 57 47 62 75

28 69 41 50 34 52 44 77 43 46 32 27 21 56 52

a.state appropriate null and alternative hypotheses.

b. use the test statistic approach to test the null hypotheses with = 0.025 (critical value)

CORRECT ANSWER IS -t = -2.0452 . PLEASE EXPLAIN HOW THEY GOT THIS ANSWER

c. calculate the test statistic

t= -1.78 (PLEASE EXPLAIN HOW THEY GOT THIS ANSWER.

d. state the conclusion (reject or dont due to sufficient or insufficient evidence).

Solution

A)

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   55  
Ha:    u   <   55 [answer]

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b)  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    29          
tcrit =    -   2.045229642   [ANSWER]

This tcrit is obtained usinga t-table or technology, while matching the degrees of freedoma and significance level.

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c)
              
Getting the test statistic, as              
              
X = sample mean =    49.86666667          
uo = hypothesized mean =    55          
n = sample size =    30          
s = standard deviation =    15.80426248          
              
Thus, t = (X - uo) * sqrt(n) / s =    -1.7790406   [answer]

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d)
              
As t > -2.0452, we   FAIL TO REJECT THE NULL HYPOTHESIS.   [ANSWER]      
      
Thus, there is no significant evidence that the average of those who default on their mortgage is less than 55. [conclusion]