2. A random sample of size n=1100 is selected this population. After a treatment is administered to the individuals in the sample, the sample mean is found to be X= 51. Do a two- tailed z-test, using a = .05. Specifically: a. *What is the null hypothesis, Ho? b. *What is the research hypothesis, Ho? c. What is the mean of the distribution of sample means, UM?P . What is the standard error of the mean, GM? Is the distribution of sample means normally distributed? (yes or no) Should we use the Unit Normal Table for the distribution of sample means? Why or why not? What is the z-score of the sample mean? *From the Unit Normal Table, what are the critical values of z, given OL = .05, two-tailed? Sketch the distribution of sample means and indicate where the sample mean is. *Also indicate where the critical values of z are, and what the area under the curve is for each tail. *Can you reject the null hypothesis, HO? (yes or no) *Can you conclude that the treatment has an effect? (yes or no) *What is the probability that you are making an error by concluding that the treatment has an effect?\" a a