A random sample of n = 12 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 = 74.5 with SS = 297. 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 the sample data, does the treatment have a significant effect? Use a two-tailed test with α = .05.
A random sample of n = 12 individuals is selected
from a population with μ = 70, and a treatment is
administered to each individual in the sample. After
treatment, the sample
with SS = 297.
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 the sample data, does the treatment have a
significant effect? Use a two-tailed test with α = .05.
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