A researcher claims that the average age of people who buy theatre tickets is 43. A sample of 30 is selected and their ages are recorded as shown below. The standard deviation is 6. At a = 0.01 is there enough evidence to reject the researcher's claim? Show all work.
43, 45,43, 45, 41 36
42, 37, 43, 37,24, 39
40, 46, 42, 47, 41, 37
38, 43,79, 41, 47, 45
37, 35, 39, 39, 37, 36