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A normally distributed population has a mean of µ = 70 and a standard deviation of...

A normally distributed population has a mean of µ = 70 and a standard deviation of σ = 12. A sample (n = 36) is selected from a population and a treatment is administered to the sample. After treatment, the sample mean is found to be M = 65.  Does this sample provide evidence of a statistically significant treatment effect with an alpha of 0.05 (non-directional hypothesis)?  [G&W Chp 8]

Yes, our z-score reaches the critical region.

No, our z-score fails to reach the critical region.

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Answer #1

for 0.05 level critical region z=-/+1.96

here as we know that z score=(X-mean)*sqrt(n)/std deviation=(65-70)*sqrt(36)/12=-2.5

correct answer is : Yes, our z-score reaches the critical region

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