Short Answer: Please make sure to use complete sentences and answer all parts of the question.

For some questions, it might be appropriate to use other answer formats, such as tables, graphs,

charts, etc. Put answers into YOUR OWN WORDS.

1. What 3 things does the central limit theorem indicate about the sampling distribution

of the means?

2. Describe the conditions under which you compute a simple z score vs a sample mean z score.

Think about what you need to know to compute each statistic.

Computational: Make sure to attach scrap paper showing all the calculations (i.e., your “work”)

for all mathematical procedures. Will receive half-credit if they do not include scrap paper.

Scenario: A behavioral psychologists, Dr. Beach, believes he has found the secret to weight

loss. To study his new program, he recruits 40 people. He then randomly assigns half of

participants to use his new program. The remaining participants are assigned to use his rival,

Dr. Body’s, fitness program. At the end of three months, the number of pounds lost for each

individual in both conditions is recorded. Below you will see the raw scores for participants

in Dr. Body’s program.

Number of Pounds Lost by Dr. Body Participants

2, 5, 7, 9, 10, 4, 4, 12, 2, 13, 7, 8, 10, 6, 2, 17, 20, 5, 8, 12, 15, 9, 7, 2, 4

1. Calculate the following for the sample above:

N=

M=

sx =

2. Calculate the z score and identify corresponding areas associated with that value.

X=6

Z=

a. What percentage of scores are BELOW this z score?

b.What percentage of scores are ABOVE this z score?

c. What is the relative frequency of this z value?

3. Calculate the z score and identify corresponding areas associated with that value.

X = 12

Z=

a. What percentage of scores are BELOW this z score?

b. What percentage of scores are ABOVE this z score?

c. What is the relative frequency of this z value?

4. Calculate the z score and identify corresponding areas associated with that value.

X=9

Z=

a. What percentage of scores are BELOW this z score?

b.What percentage of scores are ABOVE this z score?

c. What is the relative frequency of this z value?

5. Calculate the z score and identify corresponding areas associated with that value.

a. X = 4

Z=

i. What percentage of scores are BELOW this z score?

ii. What percentage of scores are ABOVE this z score?

iii. What is the relative frequency of this z value?

6. Now, imagine that we know that the population of pounds loss by dieters over a 6 month span is

= 6.5 x = 3.75.

a. What is the standard error of the mean for the sample?

b. What is the sample mean z score?

c. What is the relative frequency of this z value?

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