MA155 Statistical Reasoning
Test—Chapters 1 and 2 (fall 2009)
Name____________________________
100 pts.
Multiple Choice—Circle the correct answer. (2 points each)
1.
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A concerned parent wants to determine the amount of time spent on the phone by her child’s friends. Select
the sample most representative of the population of interest.
a. The results of a national poll of 1800 students in the same age group as the child.
b. The answers to the question by the parent(s) of 10 of his friends.
c. The answers to the question by 10 of the friends.
d. The phone records of 10 friends from the child’s group of friends.
An employer wanted to determine the importance of health insurance as a benefit to employees. Which
sample is likely to be unbiased by personal interest?
a. A group of 30 employees from the company who had medical treatment in the past year.
b. A survey of 30 union members conducted by the union that represents workers at the company.
c. A group of 30 potential employees at the state office of employment.
The name of each contestant is written on a separate card; the cards are placed in a bag and three names are
picked from the bag. Identify the type of sampling.
a. Stratified
b. Systematic
c. Convenience
d. Simple random
e. Cluster
A political science student randomly selects 100 names form the voter list of registered Democrats and 100
from the list of registered Republicans. Identify the type of sampling.
a. Systematic
b. Cluster
c. Convenience
d. Random
e. Stratified
A teacher wanted to know the attitudes of faculty on early dismissal for Homecoming. She randomly selected
20 of the 114 faculty and asked them to circle “agree” or “disagree” on the form: “Agree/Disagree: Valuable
learning time should not be sacrificed for extracurricular social activities.” Which of the evaluation guidelines
applies best in questioning the results of this study?
a. Consider the wording of any survey.
b. Consider the type of study.
c. Consider the form of response.
d. Consider the sampling method.
Select the description that most completely classifies the variable of soft drink sizes: small, medium, large.
a. Qualitative, nominal
b. Quantitative, ordinal
c. Qualitative, ordinal
d. Quantitative, interval
Statement 1: Kim pulled weeds at the rate of 20 weeds per minute, and Jan pulled 18 weeds per minute.
Statement 2: Anna Lisa held her breath for one minute 27 seconds, and Marissa held her breath for one minute
41 seconds. Select the statement for which a ratio of the measurements is meaningful. State “neither” or
“both” if appropriate.
a. Statement 1
b. Statement 2
c. Neither
d. Both
8. Compared with a metric scale that has grams as the smallest division, a scale with milligrams as the smallest
division
a. Will guarantee measurements that are more accurate, but not necessarily more precise.
b. Will guarantee measurements that are more precise and more accurate.
c. Will guarantee measurements that are more precise, but not necessarily more accurate.
d. Will not guarantee measurements that are more accurate or more precise.
9. The actual length of a particular manufactured part is 5.4523 cm. Quality control randomly selects one of the
parts, and four different quality control technicians measure its length. Their measurements are 5.3234 cm,
5.11259 cm, 5.351 cm, and 5.45 cm. Which measurement is the most accurate?
a. 5.3234
b. 5.11259
c. 5.351
d. 5.45
Free Response—Completely answer the question and show set-ups to problems where appropriate.
10. A study tries to answer the question: What is the average miles per gallon (mpg) for all new cars? Using
Consumer Reports, a random sample of 35 new cars gave an average of 21.1 mpg. (3 pts. each)
a. Identify the variable of interest.
b.
Is the variable quantitative or qualitative?
c.
What is the implied population?
d.
Is 21.1 mpg a statistic or a parameter?
11. Categorize these measurements associated with fishing, according to level: nominal, ordinal, interval, or ratio.
(2 points each)
a. Species of fish caught: perch, bass, pike, trout
b.
Cost of rod and reel
c.
Temperature of water
d.
Guidebook rating of fishing area: poor, fair, good
12. An important part of employee compensation is a benefits package. Suppose you want to conduct a survey of
benefits packages available in private businesses in Missouri. You want a sample of size of 100. Some sampling
techniques are described below. Categorize each technique as simple random sample, stratified sample,
systematic sample, cluster sample, or convenience sample. (2 pts. each)
a. Assign each business in the Missouri business Directory a number, and then use a random number
generator to select the businesses to be included in the sample.
b.
Use postal ZIP Codes to divide the state into regions. Pick a random sample of 10 ZIP code areas and then
include all the businesses in each selected ZIP code area.
c.
Send a team of five research assistants to Manchester Street in St. Louis. Let each assistant select a block or
building and interview an employee from each business found. Each researcher can have the rest of the day
off after getting responses from 20 different businesses.
d.
Use the Missouri business Directory. Number all the businesses. Select a starting place at random, and
then use every 50th business listed until you have 100 businesses.
e.
Group the businesses according to type: medical, shipping retail, manufacturing, financial, construction,
restaurant, hotel, tourism, other. Then select a random sample of 10 businesses from each business type.
13. Scientists hired by Greenpeace (which opposes genetically engineered crops) conduct a study to determine
whether Monsanto’s new, genetically engineered soybean poses any threat to the environment. Discuss
potential bias in this study. (4 pts.)
14. A breast cancer study began by asking 25,624 women questions about how they spent their leisure time. The
health of these women was tracked over the next 15 years. Those women who said they exercise regularly were
found to have a lower incidence of breast cancer. (3 pts. each)
a. Is this an observational study or an experiment? Why?
b.
Discuss one possible source of confounding.
15. A researcher plans to conduct an experiment to determine whether a new medication can alleviate depression.
Should the experiment be single blind, double blind or neither? Explain your reasoning. (4 pts.)
16. An experimenter wants to determine the average weight of adult women. He selects a simple random sample
of 1000 women and weighs them with their clothes on. (3 pts. each)
a. Identify one likely source of systematic error.
b.
Identify one likely source of random error.
17. Japan produced 5.3 million cars in 1970 and 10.0 million cars in 1998. (3 pts. each)
a. Find the absolute change.
b.
Find the relative change.
18. Fill in the blanks. (2 pts. each)
a. If Jack weighs 40% more than Jill, then Jack’s weight is ______% of Jill’s weight.
b.
If Henry earns 45% less than Ingrid, then Henry’s salary is ______% of Ingrid’s salary.
19. Determine whether the given statement is sensible and explain why it is or is not. (3 pts. each)
a. Joe makes 20% more than Bill, so Bill makes 20% less than Joe.
b.
The bank teller claims that his errors are random even though they are always to his advantage.
20. Suppose that the cost of a statistics text was $50 in 1985 and is $85 in 2000. Find the index number, rounded to
the nearest tenth, for the 2000 price with the 1985 price as the reference value. (4 pts.)
21. Suppose a week’s worth of groceries in 1990 cost $75. Adjusted for inflation, what would these groceries cost,
to the nearest dollar in 2005? (4 pts.)
22. In 1986, the median price of a house in the U.S. was $92,000. In 2000, the median price was $187,600.
a. Convert the 1986 price to year 2000 dollars. (4 pts.)
b.
Did housing prices from 1986 to 2000 increase at a rate greater than or less than the rate of inflation?
Explain. (4 pts.)