Statistics for the Behavioral Sciences

2. (3 points). What is a sampling distribution? What type of distribution does it approximate according to the central limit theorem?

3. (6 points). Let’s say you have the distribution of the following scores: 55, 65, 55, 59, 57, 63. For the distribution M=59, sd=4. Convert each raw score into a z-score.

4.(6 points). Using your z-distribution table (Appendix B in the book), give the following values:

a.% of observations greater than a z-score of +1.87

b.% of observations between the mean and z = +0.62

c.% of observations greater than z = -1.34

d.% of observations between z = -0.34 and z = +1.05

5.(10 points). Let’s say you get a sample of last year’s Psyc 221 grades from 64 Woodbury students. The sample mean is 83 with a standard deviation of 24. The historic population mean of how all students have scored in the course is 88. Use a z-test to determine if we should accept or reject the null hypothesis that our sample mean does not differ significantly from the population mean (H0: M = μ). Calculate the standard error of the mean, the z-scorefor our sample mean (hint: this is z for a sample mean, not a raw score), and say if you’d retain or reject the null hypothesis (using a two-tailed test). Bonus question: would you retain or reject with a one-tailed test (H0: M ≥ μ) and why?