Stat 220 Autumn 2005
Basic StatisticsJ. Morita
Sample Exam Cover Page & Some Sample Problems
This is an example of text that will appear on the cover page of the midterm exam. Nine sample problems follow. These are intended to be examples of the types of problems you may be asked to solve on the exam. This set of problems is not exhaustive. That is, the exam may include problems on these or other topics we have discussed in class. Not all of the exam questions will precisely match the style of one of these sample problems.
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Exam Rules:
- This is a closed book, closed notes exam, except that each student may refer to one 8 1/2” x 11” page of notes (s)he has brought to the exam.
- Use of a calculator is allowed. However, in order to receive full credit, all computations must be shown.
- Students must clearly explain each answer to receive full credit.
- Students must follow a reasonable code of conduct. Cheating or other dishonest practices will result in an examination grade of zero. Such practices include, but are not limited to (i) making use of books, papers, or memoranda other than those authorized, (ii) speaking or communicating with other students during the examination, (iii) purposely exposing written papers to the view of other students.
A good strategy: Skim the entire exam. Then work first the problems with which you feel most comfortable. Budget your time carefully.
A normal table is attached at the end of the exam.
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- Cloud seeding (dropping ice into a cloud) may increase the amount of precipitation from that cloud. The following experiment is conducted to test this assertion. Clouds are chosen at random and seeded. The amount of precipitation from these clouds is measured a well as the precipitation from nearby non-seeded clouds.
(a) What type of variable is “amount of precipitation”? Choose from the list below all that apply here. Give a one or two sentence justification for your choice.
qualitativequantitativediscretecontinuous
nominalordinal intervalsomething else (specify) ______
(b) What type of variable is “amount of precipitation”? Choose from the list below all that apply here. Give a one or two sentence justification for your choice.
qualitativequantitativediscretecontinuous
nominalordinal intervalsomething else (specify) ______
(c) Explain briefly why the amount of precipitation was measured under clouds that were not seeded.
2. The standard deviation (SD) of all the ages of UW Seattle undergraduate students is closest to:
1 month1 year5 years18 years25 years
Give a one or two sentence justification for your choice.
3. The frequency distribution of the amount of claims on automobile insurance policies is given below for January 2004. Draw a histogram for the relative frequency distribution of the amount of claims. Be sure to label axes and indicate the height of the histogram for each interval.
Amount Frequency
$00 to $200 5
$200 to $300 5
$300 to $40010
$400 to $60010
$600 to $80010
$800 to $1,20010
Total50
4. Below is the stem-and-leaf diagram for the ages in years of 15 airplanes in a major airline’s fleet.
11 | 9
10 | 0 1 5 6 9
9 | 0 0 1
8 | 5 6
7 | 1 4 6
6 | 4
5 |
What is the median age? ______
Briefly explain how you figured out your answer.
What is the mean (average) age? ______
Briefly explain how you figured out your answer.
Without computing it explicitly, what would you guess the SD to be? Justify your guess (without explicitly computing the SD.)
5. Two students in different classes take final examinations in economics. Each receives a score of 80. In one class, the average examination score was 75, and the SD was 6. In the other class, the average and SD were 74 and 8, respectively. Assume that the scores in each class follow a normal curve.
Which student did better relative to the other students in her/his class? Is this an indication that one student learned more economics than the other? If so, which one learned more? If not, then explain why not.
6. Suppose that data were collected on emphysema patients. The number of years the patient smoked and inhaled, and a physician’s subjective evaluation of the extent of lung damage were recorded. The latter variable is measured on a scale of 0 to 100.
Measurements taken on 10 patients are plotted below.
The average years smoking is about 32.
The SD of years smoking is about 9.
The average of lung damage is about 53.
The SD of lung damage is about 16.
The correlation coefficient is about 0.75.
(a)Draw the SD line.
(b)Draw the regression line.
(c)For someone smoking 36 years, what would be the regression estimate of their lung damage?
Show all of your work.
90
Lung
Damage X
70 X X
X
X X
50X
X
30 X X
Years Smoking
20 30 40 50
7. A survey was conducted to measure the effect of an advertising campaign for a certain brand of women’s shampoo. Two interviewers randomly selected telephone numbers from a telephone book and made calls between 10:00 a.m. and 3:00 p.m. to reach housewives. The first interviewer asked each housewife whether she used that brand of shampoo. The second interviewer, however, asked each housewife what shampoo she used.
Explain possible sources of bias, if any. Be explicit but concise.
8. A study was conducted to investigate the hypothesis that increased hibernation results in longer life among hamsters. 288 hamsters were monitored for the amount of time each hibernated and how long each lived. The data are plotted below.
The correlation coefficient is closest to:
-1.5 -1.0 -0.95 -0.8-0.50.0+0.5+0.8+0.95 +1.0 +1.5
Give a one or two sentence explaining how you made your choice.
*** There should be a scatter diagram here. ***
9. For each of the diagrams below, select the values that most nearly approximate the average and the SD. For at least one of parts (a), (b) or (c), indicate how you arrived at your answer. Make your choices from the following list.
0.0 0.5 1.0 1.5 2.0 2.5 3.0
3.5 4.0 4.5 5.0 5.5 6.0 6.5
(a)average = ______
SD = ______
-1.0 1.0
(b)average = ______
SD = ______
4.5 6.5
(c)average = ______
SD = ______
0.0 1.0