A random sample of n = 16 scores is selected from a normal population with a mean of μ = 50. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 54.  a) If the population standard deviation is σ = 8, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05. b) If the population standard deviation is σ = 12, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05. c)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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A random sample of n = 16 scores is selected from a normal population with a mean of μ = 50. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 54.

 a) If the population standard deviation is σ = 8, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05.

b) If the population standard deviation is σ = 12, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05.

c)Comparing your answers for parts a and b, explain how the magnitude of the standard deviation influences the outcome of a hypothesis test.