1. What is this symbol: σM ? (in words)

2. How, and why, is this term different from “S”?

3. A population has a µ = 60 and σ = 10. A sampling distribution from that population, based on samples of n = 64, will have a M of ________ and a standard error of  ___________. 

Hint: LOOK AT THE CENTRAL LIMIT THEOREM

4. Explain the relationship between distribution of sample means and normality—that is, under what circumstances is the distribution of sample means normal?

(hint: look at the central limit theorem…)

5. A sample of n = 81 scores is selected from a population with μ = 60 and σ = 9. On average, how much error is expected between the sample mean and the population mean? 

(hint: what is error in that sampling distribution that represents this population—you have all the information you need here) 

6. A random sample of n = 25 scores is selected from a population. Based on this information alone, do I know that the distribution of samples means will be normal? Why or why not?

7. All samples of size n = 49 are selected from a population with μ = 40 with σ = 12. What is the average (mean) of the distribution of sample means? (this is not a trick, it is a very simple question! The key is to understand the pieces of information you have, and which are relevant and which are not.)

8. If random samples, each with n = 16 scores, are selected from a normal population with µ = 35 and σ = 8, then what is the standard error for the distribution of sample means?

10. What happens to the standard error of M as sample size decreases (if you aren’t sure look at the basic formula for the standard error!)?

11. Which combination of two things will produce the smallest value for the standard error, and why (answering why is worth half the points of this question)? (again, look at the formula….)

12. A random sample of n = 25 scores is obtained from a population with a mean of µ = 62 and a standard deviation of σ = 10. If the mean of that sample (drawn from the population) is M = 78, what is the z-score for the sample mean in its own sampling distribution (hint: if the pop mew is 80, what is the mean of the sampling distribution?) Start by finding the standard error….

13. I have a sample of size n = 49, with a sample mean of M = 45. Based on the empirical rule, is it likely or not likely that it comes from a population distribution with a mean of Mew = 50 and an SD of 10? Calculate the Z score for the sample mean and state your conclusion and say why or why not you would say the M does or does not come from the pop with the mew of 50.