Is the sample mean an especially unlikely result


Problem

Suppose that a researcher developed a drug that she claims increases extroversion. A sample of n=4 participants has a sample mean of M=115 on a personality assessment af... Suppose that a researcher developed a drug that she claims increases extroversion. A sample of n=4 participants has a sample mean of M=115 on a personality assessment after taking the drug. The personality test has a population mean of μ=100 and σ=30. Is the sample mean an especially unlikely result based on the population parameters for the personality test? What if the researcher increased the sample to n=25 and observes the same sample mean of M=115?

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