To evaluate the effect of a treatment, a sample is obtained from a population with a mean of μ = 30, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 31.3 with a standard deviation of σ = 3.   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?

A First Course in Probability (10th Edition)
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To evaluate the effect of a treatment, a sample is obtained from a population with a mean of μ = 30, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 31.3 with a standard deviation of σ = 3.

 

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?

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