12. A random sample is selected from a normal population with a mean of 40 and a...

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12. A random sample is selected from a normal population with a mean of 40 and a standard deviation of 10.

After a treatment is administered to the individuals in the sample, the sample mean is found to be M 42.

a. How large a sample is necessary for this sample mean to be statistically significant? Assume a twotailed test with = .05

b. If the sample mean were M 41, what sample size is needed to be significant for a two-tailed test with

= .05.

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