To evaluate the effect of a treatment, a sample is obtained from a population with a mean of μ = 75, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M =79.6 with a standard deviation of s = 12.
a. If the sample consists of n = 16 individuals, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α =.05?
b. If the sample consists of n = 36 individuals, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α =.05?
c. Comparing your answer for parts a and b, how does the size of the sample influence the outcome of a hypothesis test?
Question
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 the sample data, does the treatment have a significant effect? Use a two-tailed test with α =.05.
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