INTRODUCTION TO STATISTICS

INFORMATION ON THE SECOND MIDTERM EXAMINATION

SECTION 1
DATE	October 23 (Friday)
TIME	8:00-9:05
PLACE	SCI. 3610

Examination Type: Closed notes and books. But you will be allowed to use one sheet of paper (information sheet) with the formulas and facts that you need (This sheet should not have solutions of problems or examples)

Coverage: Section 2.5 - 4.4 (included)

The important topics that you should know for the exam.

2. Looking at Data: Relationships

2.5 Relations in Categorical Data

Finding marginal and conditional distributions on and Simpson's Paradox

2.6 The Question of Causation

3. Producing Data

3.1 First Steps

exploratory analysis and statistical inference

types of data

sampling and experiments

observational and experimental studies

3.2 Design of Experiments

determination of units, factors, treatments, response variable(s)

three principals of design of experiment (control, randomization, replication)

3.3 Sampling Design

population and sample

determination of a design of a sample (probability sampling design, simple random sampling, stratified random sampling) biased samples

3.4 Toward Statistical Inference

determination of parameter and statistic

biased and unbiased statistics to estimate parameters

variability of estimates

4. Probability: The Study of Randomness

4.1 Probability Models

Relative frequency and subjective probability

Determination of sample space (S)

Rules of probability

Finding P(A^c), P(A or B) (for disjoint and not disjoint events), P(A and B)

Independence (verifying A and B independent or not, finding probabilities given independence)

4.2 Random Variables

discrete and continuous random variables

given a probability distribution finding event probabilities

constructing a probability distribution

4.3 Mean and Variances of Random Variables

given a probability distribution finding mean, variance and standard deviation

4.4 Probability Laws

finding P(A or B), P(A and B)

conditional probabilities (finding P(B|A))

construction of a tree diagram

Bayes's Rule

1. It is hard to lose weight. People spend a lot of money on weight-loss programs. Can a simple and inexpensive program do just as well as an eloborate and expensive program? You want to compare two weight-loss programs:

Program A: (Minimal program) Subjects meet with a counselor who offers advice on how to lose weight gradually through exercise and sensible diet. A second meeting with the counselor is scheduled 10 weeks later to discuss the subject's progress in losing weight.

Program B: (Standard program) Subjectts meet with a counselor once a week for 10 weeks. They are weighted each week, and the counselor offers encouragement and more elaborate advice on weight-control strategies.

a. Is this an experiment? Why or why not?

b. What are the experimental units?

c. There is one factor (explanatory variable). What is it, and what are its levels?

d. What is the response variable?

2. In astudy of the effects of acid rain, a random sample of 100 trees from a particular forest are examined. Forty percent of these show some signs of damage.

a. What is the population? what is the sample?

b. What is the parameter of interest?

c. What is the statistics?

3. A group of 2000 randomly selected adults were asked if they are in favor of or against abortion. The following table gives the results of this survey.

	IN FAVOR	AGAINST
MALE	490	410
FEMALE	650	450

If one person is selected at random from these 2000 adults, find the probability that this person is

a. in favor of abortion

b. against abortion

c. in favor of abortion given the person is a female

d. a male given the person is against abortion

e. female or in favor of abortion or both.

f. Are the events "female" and "favor" independent? Why or why not?

4. City crime records show that 20% of all crimes are violent, and 80% are nonviolent. 90% of violent crimes are reported. On the other hand 70% of nonviolent crimes are reported.

a. What is the probability that the crime will be reported?

b. If a crime in progress is reported to the police, what is the probability that the crime is violent?

5. The following is the probability distribution for the number of items lost daily on the buses of the Suburban Pupil Transit Lines:

Number of items lost daily	1	2	3	4	5	6	7
Probability	0.05	0.43	0.17	0.25	0.06	0.03	0.01

a. Find the mean and standard deviation

b. What is the probability that at most 4 items will be lost on a given day?

6. The following table gives the probabilities that a randomly selected individual falls into 6 sex-by-cholesterol level classes.

Cholesterol level (in mg)	Below 200	200-240	Above 240
Female	.055	.210	.135
Male	.037	.263	.300

a. What is the probability that the individual is female?

b. What is the probability that the individual is either a male or has a cholesterol level above 240?

c. What is the probability that the individual is female given that her cholesterol level is above 240 mg.?

d. What is the probability that the individual has a cholesterol level above 240 mg. given that the individual is a female?

e. Are the events "being female" and "having above 240 cholesterol level" independent? Please justify your answer.

7. Based on many geological surveys, an energy company has classified geological formations beneath potential oil wells as types 1, 2, and 3. For a particular site in which the company is considering drilling for oil, the probabilities of 0.35, 0.40, and 0.25 are assigned to the three types of formations, respectively. It is known from experience that oil is discovered in 40% of type 1 formations, in 20% of type 2, and in 30% of type 3 formations.

a. Draw a tree diagram that summarizes this information.

b. What is the probability that the oil will be discovered at this site?

c. If the oil is not discovered at this site, dtermine the probability of it being type 1 formation.

d. Are the events "discovering oil" and " the formation being type 1" independent? are these events mutually exclusive? Please justify your answer.

---