The owner of an Axion health club franchise believes that the average age of her members is under 55 years. To test this, a random sample of 30 was selected; the following sample data are 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.