AP Statistics / Mr. Hansen
9/22/2000

Name: ______________________________

1.

Categorize each of the following distributions as normal, skew left, skew right, uniform, or other. Draw a believable box plot or histogram in each case.

(a)

Distribution of die rolls (1 fair die)

(b)

Distribution of dice rolls (2 fair dice)

(c)

Residential real estate sale prices for single-family homes in a metropolitan area

(d)

Salaries of all citizens in the Washington, D.C., metropolitan area

(e)

Salaries of civilian federal government workers in the Washington, D.C., metropolitan area

(f)

Lifetimes of TV shows

(g)

Lifetimes of human beings

(h)

Heights of human beings

2.

Categorize each pair of variables as being positively associated, negatively associated, or other. Mark with an asterisk (*) those that are probably linear.

(a)

Height vs. shoe size

(b)

Height vs. weight

(c)

GPA vs. TV watching time

(d)

GPA vs. last digit of phone number

(e)

Boredom level vs. number of hours spent watching Olympics

(f)

Height above ground vs. time (in seconds) for a cannonball fired upward from the earth’s surface

(g)

Height above ground vs. time (in seconds) for a cannonball fired horizontally from a high platform

3.(a)

State Chebyshev’s Theorem for the fraction of observations in the interval m ± xs.

(b)

Why is x > 1 an obvious requirement in Chebyshev’s Theorem?

4.

How can one show a categorical variable on a scatterplot?

5.

Why are there no generally accepted criteria for outliers in bivariate relationships?

6.

Somewhat advanced bonus question: As you may know, the Rand function on your TI-83 (press MATH key, choose PRB, then #1) can be used to generate a random real number between 0 and 1. Describe a process that could be used to generate random z scores that closely conform to the standard normal distribution. (In other words, about 68% of the values so generated should be between –1 and 1, about 95% of the values should be between –2 and 2, and so on. There should be a noticeable bunching near 0 and a trailing out toward both +¥ and –¥.)

7.

Super-advanced bonus question; calculus helpful but not required: As you know, the NQP is a useful tool for checking the normality of a data set, because the NQP displays a nice straight line if the underlying distribution is truly normal (or nearly so). Describe a process for checking how closely a data set matches the following highly non-normal distribution function: f (x) = 0.5(x – 2)^–1/2, on the interval (2, 3]. In other words, the domain of f is {x: 2 < x £ 3}.