A researcher claims that average age of people who purchase theatre tickets is 50. A sample of 30 is selected and their ages are recorded as shown below. The standard deviation is 8. At a = 0.01 is there enough evidence to reject researcher's claim? Show all work.
50 46 33
48 44 49
46 44 71
53 46 49
57 60 58
51 56 50
73 53 45
52 78 60
52 59 66
59 51 59