UNIVERSITY OF MINNESOTA, MORRIS


INTRODUCTION  TO STATISTICS (GENED WEB)
Stat 1601

MIDTERM EXAMINATION

Summer 2006

Instructions:

Read each question carefully before selecting the best answer. There is a total of 47 questions on the exam. Prepare your answers and email them to stat1601@cda.morris.umn.edu by the due date of
    July 13, 2006 (Thursday) 6 pm (central).
Good luck.

 

Questions 1-5 use the following information. The stemplot below gives the age of female Oscar winner actor between 1928 and 1996..

1. What is the median of this data set?
(a) 35.9
(b) 34.0
(c) 30.0
(d) 33.5
2. What is the interquartile range for this data?
(a) 11
(b) 60
(c) 13
(d) 28
3 . According to 1.5xIQR criterion above which one of the following values you can locate suspected outliers?
(a) 16,5
(b) 50
(c) 49
(d) 55.5
 
4. What is the best measure of spread for this distribution?
(a) Variance
(b) Interquartile Range
(c) Standard Deviation
(d) Sum of Squared Residuals
5. What are the names of the female actors whose ages are suspected outliers based on the 1.5xIQR criterion? Click here to view the data set.
 

For problems 6-10 use the following information:
A social science department at a major research university has applicants for admission with GRE scores that average 544 with a standard deviation of 103. These GRE scores are distributed normally.

6. What proportion of applicants have scores over 700?
(a) .0655
(b) .0228
(c) .9772
(d) .9345
7. What test score is at the 15th percentile of the GRE distribution?
(a) 559.4
(b) 436.9
(c) 320.5
(d) 651.1


8. What proportion of scores are between 500 and 720?
(a) .9838
(b) .9568
(c) .8997
(d) .6228


9. Suppose the department ignores all applicants with GRE scores under 500. What proportion of applications are ignored?
(a) .6628
(b) .6664
(c) .3372
(d) .3336


10. What GRE score should be used as a cutoff if the department wishes to ignore the lowest 30 percent of applicants?
(a) 490.44
(b) 574.90
(c) 350.36
(d) 737.64

Use the following statistics package output (WEBSTAT) below for problems 11-15:
The data show the relationship between the age of a grandfather clock(in years) and its auction price(in $). The scatterplot contains information on 32 clocks.

Simple linear regression results:
Independent variable: age
Dependent variable: auctionprice
Sample size: 32
Correlation coefficient: 0.7031
(See fitted line plot in Graphics Panel.)

Estimate of sigma: 264.7873

Parameter Estimate Std. Err DF Tstat Pval
Intercept -67.16766 255.92143 30 -0.26245424 0.7948
age 9.402623 1.735951 30 5.4164104 1.0E-5

 
11. If a clock had an age 0f 110 and an auction price of $2150, which is the best description of this point?
(a) The point is an outlier, and is not influential.
(b) The point is an outlier, and influential.
(c) The point is not an outlier.
(d) The point is not infuential.

12. Interpret the correlation coefficient and the value of squared correlation (R-sq).
13. Interpret 9.402623
14. Use the equation for the least squares line to predict the auction price of a clock that is 150 years old.

15. Suppose the auction price of a clock with an age of 150 years was $1,522. What is the value of the residual for this observation?
 
16. Insect traps of two colors (white, green) were placed in a small grain field. The numbers of bugs caught in the white traps were 21,12,14, 17,13,17. The numbers of bugs caught in the green traps were: 37, 32, 15, 25, 39, 41.
    • Using appropriate graphical and numerical methods to assist you, address the following question. Which color trap catches more bugs? Your answer must include graph(s) (a stemplot can be typed easily in your email message to us), appropriate numerical summaries, and an appropriate written argument that uses the graphical and numerical summaries.
    • This question is worth three points: one for the graph(s), one for the numerical summaries, and one point for the written statement.
17. Suppose a club has both student and faculty members. The club leadership wishes to survey the membership about an upcoming event, and they decide to take separate samples of students and faculty club members. A simple random sample of six student members gives the following subjects: Bakken, Bandas, Dorale, Dosch, Redlin, Shea. A simple random sample of three faculty members gives the following subjects: Guyotte, Lawrence, Ng.
What is the name of the sampling design that was used to survey the club membership?
For the Questions 18-21 consider the following situation:

Does using a cell phone while driving make an accident more likely? Researchers compared telephone company and police records to find 699 people who had cell phones and were also involved in an auto accident. Using phone billing records, they compared cell phone use in the period of the accident with cell phone use the same period on a previous day. Result: the risk of an accident was 4 times higher when using a cell phone.

18.This study is

  1. a randomized comparative experiment
  2. an experiment, but without randomization
  3. a simple random sample
  4. an observational study, but not a simple random sample
19. The explanatory variable in this study is
  1. whether or not the subject had an auto accident
  2. whether or not the subject was using a cell phone
  3. the risk of an accident
  4. whether or not the subject owned a cell phone

20. The researchers also recorded the manufacturer of each subject's cell phone (Motorola, Nokia, and so on). This variable is

  1. a qualitative variable
  2. a continuous variable
  3. a quantitative variable
  4. a measurable variable

21. An example of a lurking variable that might affect the results of this study is:

  1. whether or not the subject had an auto accident
  2. whether or not the subject was using a cell phone
  3. whether or not the subject was talking to a passenger in the car
  4. whether or not the subject owned a cell phone
For the questions 22 to 24 consider the following situation:

A researcher studied whether friendship affects the prices people set for selling things. She had 80 students all imagine selling the same six items. Half the students, assigned at random, imagined selling the items to a stranger. The other half imagined selling the items to a friend. Then the students were asked to set the price of the items. On the average, those selling to friends set lower prices than those selling to strangers.

22. This study is
  1. a randomized comparative experiment
  2. an experiment, but without randomization
  3. a simple random sample
  4. an observational study, but not an SRS
23. This study applies the principle of replication in
  1. assigning subjects at random
  2. having the students imagine selling six items
  3. using 80 students rather than just a handful
  4. comparing two treatments (selling to friends or strangers)
24. To randomly assign 40 of the 80 students to the "friends" group, we must first label them, then use the table of random digits. Which of these are correct ways to label?
  1. Label the 80 students 01 to 80
  2. Label the 80 students 00 to 79
  3. Label the 40 students in the "friends" group 01 to 40
  4. All three are correct
  5. (a) and (b) are correct but (c) is not

 

25. The life span of the Everrun Batteries used in an application is normally distributed with a mean of 3.5 years and a standard deviation of .4 years. The manufacturer of these batteries decides to replace any battery that dies before the guarantee period is up and wants to set the length of that period so that no more than 5% of the batteries will have to be replaced. How long should the guarantee period be so that no more than 5% of the batteries will die?

26.

  1. A random sample of 25 college students is surveyed about their political views. Five of them have liberal views. Define the parameter of interest and the statistic to estimate this parameter.
  2. There are 548 students enrolled in the management program at a state university, and 212 ofthem are planning to go to a graduate program. A random sample of 100 students is selected. In this sample 20 of them were planning to go to a graduate program. Define the parameter of interest and the statistic to estimate this parameter and give their values.

For the questions 27 to 33 consider the following information:

The table below gives the results of a study to determine better treatments for cocaine addiction. There are three treatments, despramine, lithium, and placebo.

 

Relapse to Cocaine?

Treatments

Despramine

Lithium

Placebo

Yes

10

18

20

No

14

6

8

27. What is the probability that the subject did not receive placebo?

28. Suppose that 2 of the subjects are randomly selected, what is the probability that both of them receieved placebo?

29. What is the probability that the subject was on the placebo treatment or had a relapse?

30. Find the probability that the subject was in the placebo group given that there was no relapse into drug use.

31. Find the probability that the subject had a relapse given that they were on the Despramine treatment.

32. Are the events "being on lithium treatment" and "having a relapse" disjoint? Are they independent? Please justify your answer to receive a credit.

33. Are the events "being on lithium treatment" and "being on despramine treatment" independent? Are they disjoint? Please justify your answer to receive a credit.

For the questions 34 to 35 consider the following information:

According to the Arizona Chapter of the Lung Association, 7.0% of the population has a lung disease. Of those having lung disease, 90.0% are smokers; and of those not having lung disease, 25.3% are smokers.

34. Determine the probability that a randomly selected smoker has a lung disease.

35. Determine the probability that a randomly selected non-smoker does not have a lung cancer.

 

36. An investor plans to invest $50,000 in one of four investments. The return on each investment depends on whether next year's economy is strong or weak. The following table summarizes the possible payoffs, in dollars, for the four investments. 

Next Year's Economy

Investment

Strong

Weak

Certificate of Deposit

6,000

6,000

Office Complex

15,000

5,000

Land Speculation

33,000

-17,000

Technical School

5,500

10,000
Assume that next year's economy has a 40% chance of being strong and a 60% chance of being weak. Which investment has the best expected payoff? Which one has the worst? Which investment would you select? Explain your answer.

For the questions 37 to 40consider the following information:

The Arizona state lottery, Lotto, is played as follows: The player selects six numbers from the numbers 1-42 and buys a ticket for $1. There are six winning numbers, which are selected at random from the numbers 1-42. To win a prize, a Lotto ticket must contain three or more of the winning numbers. Following is a probability distribution for the number of winning numbers for a single ticket.  

Number of winning numbers

0

1

2

3

4

5

6

Probability

0.3713060

0.4311941

0.1684352

0.0272219

0.0018014

0.0000412

0.0000002

37. Determine the mean and the standard deviation.

38. If you buy one Lotto ticket, determine the probability that you win a prize.

39. If you buy one Lotto ticket per week for a year, determine the probability that you win a prize at least once in the 52 tries.

40. If you have more than 1 winning numbers on a ticket, what is the probability you have 3 winning numbers on that ticket?

 

41. A somewhat absent-minded hiker forgets to bring her insect repellent on 30% of his hikes. The probability of being bitten is 90% if he forgets the repellent, and 20% if she uses the repellent. What is the probability that she forgot her repellent given that she was bitten.

 

42. An airline knows that 10% of the people holding reservations on a given flight will not appear. The plane holds 18 people. If 20 reservations have been sold, find the probability that the airline can accommodate everyone appearing for the flight.

For the questions 43 to 45 use the following information:

According to tables provided by the U.S. National Center for Health Statistics in Vital Statistics of the United States, there is about an 80% chance that a person age 20 will be alive at age 65. Suppose 15 people age 20 are selected at random.

43. Find the probability that the number alive at age 65 will be exactly five.

44. Find the probability that the number alive at age 65 will be at least five.

45. Suppose that 200 people selected at random. What is the probability that the proportion of them alive at age 65 will be more than 50%?

For the questions 46 to 47 use the following information:

Gestation period of humans are normally distributed with a mean of 266 days and a standard deviation of 16 days. Suppose that we observe the gestation periods for a sample of nine humans.

46. Find the probability that the average gestation period for the nine humans selected is more than 270 days.

47. Find the probability that the average gestation period for the nine humans is less than 250 days.