MAKE SURE TO SHOW YOUR WORK!

1. What are the three characteristics of a normal curve?

2. What percentage of cases are lower for each of these z-scores: -1, -2, -1.75, 1, 2, 1.75

-1 =

-2 =

-1.75 =

1 =

2 =

1.75=

3. For a data set with Mean = 20, SD = 3 find the Z scores for each of the following raw scores: 23, 17, 15, 22, 30.

23:

17:

15:

22:

30:

4. Look at your result from the previous question in regards to raw score 15. Color-in the space that represents the area for persons who fall below the raw score of 15.

5. Using your answers from number 3, what percentage of scores fall between raw scores 17 and 22 (hint: This is a harder one, it helps to use the same steps you used in question 4). Would the distance be the same between scores of 22 and 27?

6. When or why might you convert raw data to z scores?

7. Briefly define each of the following:

a. Distribution of sample means

b. Expected value of M

c. Standard error of M

8.A sample is selected from a population with a mean of =40 and a standard deviation of8. (Hint: When we take a sample, we expect the mean to be the same as the population means. Use the equation for standard error.)

a. If the sample has n=4 scores, what is the expectedvalue of M and the standard error of M?

b. If the sample has n=16 scores, what is the expectedvalue of M and the standard error of M?

9. A population has a standard deviation of30. (Hint: use the equation for standard error.)

a. On average, how much difference should existbetween the population mean and the sample meanfor n=4 scores randomly selected from thepopulation?

b. On average, how much difference should exist for asample of n=25 scores?

c. On average, how much difference should exist for asample of n=100 scores?

10. State the definition of Type 1 and Type 2 errors and provide examples for each.