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 \(\alpha=.05\)
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 \(\alpha=.05\)
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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