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 obligations 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 age of those who do is 55 years. To test this, a random sample of 30 who had defaulted was selected; the following sample data reflect the ages of the sampled individuals:

40 55 78 27 55 33 51 76 54 67 40 31 60 61 50 42 78 80 25 38 74 46 48 57 30 65 80 26 46 49

a. State the appropriate null and alternative hypotheses.

b. Use the test statistic approach to test the null hypothesis with a  0.01.