1. (10) Distinguish between a statistic and a parameter and give two examples of each.

2. (6) Give an example of a data set where the median is a more "typical" value than the mean.

3. (3) Why can’t (S (x - ü ))/n be used as a measure of dispersion for a sample?

4. (6) Give two reasons for taking the square root in the formula for standard deviation.

5. (30) Stuart Smalley is the quality control manager of a company that manufactures automobile thermostats and heater cores at two separate locations, one in Ohio, the other in Alabama. Each location produces the parts on a total of twenty assembly lines. Stu wants to estimate the number of rejected parts per week each assembly line produces. He randomly chooses the weeks of October 16, 23, and 30 as sampling weeks and picks three assembly lines at the Ohio plant. At 4:30pm Friday of the each of the weeks, he asks the line foremen for a count of rejected parts.. The numbers obtained were 17, 4, 2, 6, 4, 3, 3, 7, 1.

a. (3) What is the population in this study?

b. (2) What is your best guess as to the shape of this population?

c. (4) What parameter about the population is Stuart trying to obtain, and what symbol is used for this?

d. (3) What is the sample (use the definition I did in class, not the textbook’s!)?

e. (2) What are the elementary units?

f. (4) Calculate the sample mean. (Show your work!)

g. (2) What is the sample median?

h. (4) Calculate the sample standard deviation? (Show your work!)

i. (6) Comment on problems with external and internal validity.

6. (15) Use a truncated power series expansion for exp(u) around u=0:

(*)

to find the proportion of area under the normal curve between the mean and 0.8 standard deviations above the mean. Proceed thusly: Find the first four terms of the truncated expansion for

by substituting u=-z^2/2 in (*) and then integrate the resulting sixth degree polynomial. Calculate the result to four decimal places and compare this with the value from the standard normal table provided.

7. (30) SAT composite scores are normally distributed with m = 1017 and s = 207.

a. What is the probability that a randomly selected SAT score is between 900 and 1100?

b. What is the probability that a randomly selected SAT composite score is less than 900?

c. What is the probability that a randomly selected SAT composite score is greater than 1400?

d. What is the 90th percentile of SAT composite scores?

e. Between what two numbers are the middle 95% of SAT composite scores?