SOLUTION: You want to prove that a population mean is not 7. Data is ratio and a large sample size will be used (n = 225). When the sample is done the sample mean is computed to be 7.2 an

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Question 286095: You want to prove that a population mean is not 7. Data is ratio and a large sample size will be used (n = 225). When the sample is done the sample mean is computed to be 7.2 and the sample standard deviation is 1.5. Test the hypothesis using an alpha of 5%. Use formal hypothesis testing and compute the p-value.

Found 2 solutions by stanbon, jrfrunner:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
You want to prove that a population mean is not 7.
Data is ratio and a large sample size will be used (n = 225).
When the sample is done the sample mean is computed to be 7.2 and the sample standard deviation is 1.5.
Test the hypothesis using an alpha of 5%.
Use formal hypothesis testing and compute the p-value.
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Ho: u = 7
Ha: u is not 7 (claim)
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t(7.2) = (7.2-7)/1.5 = 0.1333...
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p-value = 2*P(t > 0.13333.. with df = 224)
= 2*tcdf(0.13333..,100,224) = 0.8940
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Wow! Fail to reject Ho; that p-value is much larger than the p-value.
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Cheers,
Stan H.
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Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
Ho: Mu=7.0
Ha: Mu not 7.0
Since we are testing the average and the sample size is large by the Central limit theorem we are allowed to assume normality of the averages.
test statistic Z = (Xbar - mu0)/SE = (7.2-7.0)/(1.5/sqrt(225)) = .2/0.1 = 2.0
pvalue = P (Z<-2.0) + P(Z>2.0) = 0.0228 = 0.0228+0.0228=0.0456
This represent the risk of incorrectly rejecting Ho, the alpha level is given as 0.05 therefore our risk is lower so we can reject Ho without incurring higher risks than allowed (ie reject Ho when pvalue