Population A: A computer randomly generates scores (for a given population) between 0 and 100. (Uniform distribution) The mean of the scores in population A is therefore 50 with a standard deviation of 28.8675.

Population B: A computer randomly generates scores (for a given population) between 25 and 125. (Uniform distribution) The mean of the scores in population B is therefore 75 with a standard deviation of 28.8675.

Population C: A computer randomly generates scores (for a given population) between 50 and 150. (Uniform distribution) The mean of the scores in population C is therefore 100 with a standard deviation of 28.8675.

Question # 1

You take a sample of size n = 25 from one of these populations, but you don't know which one. You get an average (scores) of 60. Null hypothesis (H0): This sample comes from population A. Alternative hypothesis (H1): This sample comes from another population where the mean is higher (i.e. -d., population B or population C).

1a. Set the null hypothesis according to the parameter of interest. Set the alternative hypothesis according to the parameter of interest. Test the null hypothesis with alpha = .05 by stating your / your / your critical value (s) of z, of x bars and make your decision and draw your conclusion.

1b. What would have been your decision and conclusion if you had drawn a sample of size n = 10?

1 C. Compare the statistical power of your test with n = 25 and that with n = 10. How could that explain your results?

1d. (1 bonus point) What is the smallest alpha value that would have allowed you to reject H0 with n = 50?