Question: A random sample of n = 36 scores is selected from a normal population with a mean of \(\mu \) = 60. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 52.

1. If the population standard deviation is \(\sigma \) = 18, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with a = .05.
2. If the population standard deviation is \(\sigma \) = 30, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with a = .05.
3. Comparing your answers for parts a and b, explain how the magnitude of the standard deviation influences the outcome of a hypothesis test.

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