SOLUTION: Could someone please help me with this problem? Thanks in advance because I am really lost on how to do this problem. A researcher claims that the average age of people who buy

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Question 677098: Could someone please help me with this problem? Thanks in advance because I am really lost on how to do this problem.
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 62 45 52 36 42 37 59 37 69 39 40 46 42
47 41 37 70 43 79 41 38 45 37 35 40 39 37 36

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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 62 45 52 36 42 37 59 37 69 39 40 46 42
47 41 37 70 43 79 41 38 45 37 35 40 39 37 36
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The mean of that sample = 45.3
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Hypothesis Test:
Ho: u = 43 (claim)
Ha: u is not equal to 43
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Rule: Reject Ho if the test statistic is < -2.5857 or is > +2.5857
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test statistic: z(45.3) = (45.3-45)/6 = 0.3/6 = 0.05
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Critical values for alpha = 0.01:: z = +-2.5758
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Since the test stat is not in the reject interval,
fail to reject Ho.
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The test results support the claim.
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Cheers,
Stan H.