SOLUTION: Need help with this one desperately! A researcher claims that the average age of people who buy theatre tickets is 40. A sample of 30 is selected and their ages are recorded as

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Question 296298: Need help with this one desperately!
A researcher claims that the average age of people who buy theatre tickets is 40. A sample of 30 is selected and their ages are recorded as show below. The standard deviation is 5. At 00 = 0.05 is there enough evidence to reject the researcher's claim? show all work.
45 38 40 45 35 37 45 43 45 48
44 38 45 44 41 45 50 45 37 39
45 46 35 41 39 41 38 39 39 55

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A researcher claims that the average age of people who buy theatre tickets is 40. A sample of 30 is selected and their ages are recorded as show below. The standard deviation is 5. At 00 = 0.05 is there enough evidence to reject the researcher's claim? show all work.
45 38 40 45 35 37 45 43 45 48
44 38 45 44 41 45 50 45 37 39
45 46 35 41 39 41 38 39 39 55
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Ho: u = 40
Ha: u is not equal to 40
Find the mean of that set of data.
I'll leave that to you.
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Call that sample mean "k"
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Find t(k) = (k-40)/[5/sqrt(30)]
Let's say that number is "m"
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Find the p-value = 2*P(t > m when df=29)
If that number is less than 5%, reject Ho.
If that number is greater tan 5%, fail to reject Ho.
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Cheers,
Stan H.