Question 844710: A random sample of n = 16 individuals is selected from a population with μ = 70, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M = 76 with SS = 960.
a. How much difference is there between the mean for the treated sample and the mean for the original population? (Note: In a hypothesis test, this value forms the numerator of the t statistic.)
b. How much difference is expected just by chance between the sample mean and its population mean? That is, find the standard error for M (Note: In a hypothesis test, this value is the denominator of the t statistic.)
c. Based on sample data, does the treatment have a significant effect? Use a two-tailed test with α = .05
What is the decision for parts a,b,and c? How would I report them in A.P.A. format?
Thank You
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A random sample of n = 16 individuals is selected from a population with μ = 70, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M = 76 with SS = 960.
a. How much difference is there between the mean for the treated sample and the mean for the original population? (Note: In a hypothesis test, this value forms the numerator of the t statistic.)
Ans: 76-70 = 6
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b. How much difference is expected just by chance between the sample mean and its population mean? That is, find the standard error for M (Note: In a hypothesis test, this value is the denominator of the t statistic.)
Ans: 960/sqrt(16) = 240
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c. Based on sample data, does the treatment have a significant effect? Use a two-tailed test with α = .05
t(76) = (76-70)/240 = 6/240 = 1/40
p-value = 2*P(t > 1/40 when df = 15) = 2tcdf(1/40,100,15) = 0.49
Since the p-value is greater than 5%, fail to reject Ho.
Conclusion: The test results does not support the claim that the
population mean is 70.
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What is the decision for parts a,b,and c? How would I report them in A.P.A. format?
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Cheers,
Stan H.
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