FOR INSTRUCTORS USE

1.

a......./3

b......./3

c......./3

d......./3

e......./3

f......./5

........../20

2.

a......./2

b......./2

c......./3

d......./2

e......./3

........../12

3.

a......./5

b......./5

........../10

4.

a......./4

b......./8

c......./6

........../18

5.

a......./5

b......./5

........../10

6.

a......./5

b......./5

........../10

7.

........../10

8.

........../10

TOTAL

........../100

1. Following are the prices of 16 models of women's running shoes along with their weights, in ounces.

Brand	Price($)	Weight
Addidas Equipment Running	100	9.9
Addidas Torsion Revenge	90	14.2
Asics Gel-121	70	9.5
Asics Gel-Eagle	65	10.5
Avia 2075	90	13.5
Avia 3020	60	9.0
Avia Meridian	80	8.9
Brooks Addition	70	11.6
Brooks Eldorado	70	11.3
Brooks Prodigy	45	8.6
Converse Ellipse	70	11.7
New Balance 530	70	9.0
Nike Air/Atlantis	80	11.5
Puma Terrain	120	13.0
Saucony Grid Courageous	95	10.7
Saucony Jazz 3000	68	9.3

a. Make a stemplot of the data for price and interpret

b. Compute the mean price for the running shoes listed above

c. Give the five-number summary of the data for price

d. Construct a boxplot for price and interpret

e. Use the 1.5xIQR criterion to spot suspected outliers for the price of 16 shoes listed above

f. The relation between the weight (x) and price (y) has been studied. The least squares regression line is y=13.4+6x.

Interpret 13.4 and 6.0

What would be the sign of the correlation coeffiecient r. Please justify your answer.

2. In September 1988 the House of Representatives voted on the amendment requiring life imprisonment for drug related murders. The probabilities associated with the results of the vote are given in the following table:

	Yea	Nay	Did Not Vote
Democrat	.35	.20	.04
Republican	.39	.00	.02

a. What is the probability that a randomly selected representative voted for the amendment?

b. What is the probability that a randomly selected representative is a Democrat and voted against the amendment?

c. What is the probability that a representative known to have voted for the amendment is a Democrat?

d. What is the probability that a representative known not to have voted is a Republican?

e. Are the events "voted for the amendment" and "being a Democrat" independent? Are they disjoint? Please justify your answer.

PLEASE ANSWER EITHER ONE OF THE FOLLOWING TWO QUESTIONS

3. A statistics professor has noted from past experience that students who do the homework for the course have a 0.90 probability of passing the course. On the other hand, students who do not do the homework for the course have a 0.25 probability of passing the course. The professor estimates that 75% of the students in the course do the homework.

a. What is the probability that a randomly selected student will pass the course?

b. Given a student passes the course, what is the probability that she or he completed the homework?

3. The Dallas IRS auditing staff is concerned with identifying potential fraudulent tax returns. From the past experience, they believe that the probability of finding a fraudulent return given that the return contains deductions for contributions exceeding the IRS standard is .20. Given the deductions for contributions do not exceed the IRS standard, the probability of a fraudulent return decreases to .02. It is also known that 8% of all returns exceed the IRS standard for deductions due to contributions.

a. What is the probability of finding a fraudulent return?

b. What is the probability that deductions for contributions exceeds the IRS standards given that the return is fraudulent?

4. The Statistical Abstract of the United States reported that the average cost per day of owning an automobile in the United states is $7.62. This includes the cost of the car, general maintenance, gasoline, and insurance. A researcher claims that college students' average daily ownership expenses are less than the national average. A random sample of 54 college students who own cars found the average cost per day to be $6.78 with standard deviation $1.77.

a. State the null and alternative hypotheses.

b. Carry out the test and give the P-value. Report your conclusion.

c. Is the result significant at the 1% level?

PLEASE ANSWER EITHER ONE OF THE FOLLOWING TWO QUESTIONS

5. A customer's group sampled 49 different stores in the city and found that the average price of a particular model and brand of washing machine was $522.85 with a population standard deviation of $29.55.

a. Find a 95% confidence interval for the average price of this particular washing machine.

b. How many observations must be averaged to get a margin of error of 5 with 95% confidence?

5. The percentage of American men who say they would marry the same woman if they had to do all over again is 80%. The percentage of American women who say they would marry the same man again is 50% (Harper's Index, 1991).

a. What is the probability that in a group of 10 married men, at least 7 will claim that they would marry the same woman again?

b. Use the normal approximation to find the probability that in a group 40 women more than 80% of them will claim they would marry the same man again.

6. Shorkey, McRoy, and Armendariz examined the relationship between the intensity of parental punishment practices and various demographic characteristics of mothers. The intensity score summary statistics are shown in the accompanying table, with higher scores showing a greater intensity of parental punishments.

GROUP	n	Sample Mean	s
Single mothers	8	70.75	14.80
Separated mothers	6	77.33	13.69

a. Is there a significant evidence that the mean intensity of parental punishment scores for single mothers is different than the mean intensity scores for separated mothers? State the null and alternative hypotheses, give the P-value. What is your conclusion?

b. Use a 95% confidence interval to estimate the difference between the mean intensity of parental punishment scores for single and separated mothers.

PLEASE ANSWER EITHER ONE OF THE FOLLOWING TWO QUESTIONS

7. A case study showed that out of 10,351 convicts who escaped from U.S. prisons, only 7,867 were recaptured (The Book of Odds, by Shook and Shook, Signet, 1993). Find a 99% confidence interval for the true proportion of all escaped convicts who will eventually be captured.

7. The Virginia State Patrol took a random sample of 225 accident reports from their files and found that 90 involved alcohol as the underlying cause. Find a 99% confidence interval for the true proportion of Virginia auto accidents due to alcohol.

PLEASE ANSWER EITHER ONE OF THE FOLLOWING TWO QUESTIONS

8. There is a traditional belief that creative individuals use psychoactive substances (for example alcohol or marijuana) to enhance their creativity. Does this really work? Lapp, Collins, and Izzo (1994), report an experiment where subjects were given alcohol or placebo. Subjects were given a pre and post test to see whether their creativity improved or not. The two-way table below gives the data.

		Creativity Improved?
		Yes	No
	Yes	18	22
Alcohol
	No	22	18

Is there an evidence to conclude that alcohol use and creativity are related at a=0.05 level? Carry out the appropriate test and report your result.

8. Psychological and social factors can influence the survival of a patients with serious diseases. One study examined the relationship between survival of patients with coronary heart disease and pet ownership. Each of 92 patients was classified as having a pet or not and by whether they survived for 1 year. Here are the data. (Friedmann et al. (1980)

		Pet ownership
		No	Yes
	Alive	28	50
Patient status
	Dead	11	3

Is there an evidence to conclude that pet ownership and patient status are related at a=0.05 level? Carry out the appropriate test and report your result.