Chapter 5 Review-KEY
Name:______________________________
Directions: Answer the questions completely; use your notes, homework and textbook.
1. Explain what is meant by the placebo effect.
When a member of a control group who receives an inactive placebo actually improves.
2. Explain what is meant by a sample statistic.
Numbers that summarize the raw data.
3. Explain what is meant by an observational study.
Members of the study are observed, but not influenced by the researchers.
4. Give an example of raw data.
In a study of the average weight of all first graders, the weights of every first grader in the sample group.
5. Give an example of a sample statistic.
The average weight of all first graders in the sample group.
6. Identify the sampling method (simple random sampling, systematic sampling, convenience sampling,
and stratified sampling) in the following study. Every 200th quart of ice cream off the assembly line is
tested for taste and consistency.
Systematic sampling
7. For the following question identify which type of statistical study is most likely to lead to an answer.
Explain. Do guests at Walt Disney World weigh more than the average population?
Case-control study
8. For the following question identify which type of statistical study is most likely to lead to an answer.
Explain. Who will be chosen freshman class president?
Observational study
9. For the following question identify which type of statistical study is most likely to lead to an answer.
Explain. Do grocery store shoppers prefer Coke or Pepsi?
Single-blind experiment
10. A survey finds that 45% of Americans spend less than 2 hours a day watching television, with a
margin of error of 5%. Interpret these results.
We can be 95% confident that 40% to 50% of Americans spend less than 2 hours a day watching TV.
11. Explain what is meant by participation bias.
Participation bias occurs when participation in a study is voluntary because people who feel strongly are
more likely to volunteer.
12. Why is it important to consider the source of a study?
Because the study may be biased in favor of those who are carrying it out.
13. Give an example that illustrates the meaning of availability error. Explain your example.
A survey question that asks whether your favorite cola is Coke or Pepsi has an availability error because
someone may have answered Sprite if given an open ended question.
14. Give an example of selection bias. Explain your example.
A magazine calling all of its subscribers to ask if they are satisfied with their articles has a selection bias
because subscribers are more likely to be satisfied with the content of the magazine.
15. In what way might the following study be flawed?
The National Dairy Council sponsored a study that concluded consuming milk or yogurt or cheese three
times a day would help with weight loss.
Since the Dairy Council paid for the study, the scientists might be more likely to find results in favor of
consuming dairy.
16. In what way might the following study be flawed?
A study concluded that video games that were twice as violent as others caused behavior problems in
teens.
The variables of interest are not well-defined. What does “twice as violent” mean? How did the
researchers define “behavior problem”?
17. How would you select an unbiased sample for the following study?
Which candidate for governor is most likely to win the next election?
A phone poll of registered voters throughout the state.
18. Why do you think it is sometimes difficult to define the variables of interest of a study? Give an
example of a variable of interest that is difficult to define.
It can be difficult to define a quantity of interest when it is a part of the population that is difficult to reach.
For example, it would be difficult to estimate how many people were not counted in the last census.
19. Give an example of qualitative data.
Brand names of shoes worn by students
20. Explain the differences between a bar graph and a histogram.
Bar graphs display qualitative data and the bars do not touch. Histograms display quantitative data and
the bars do touch.
The following table shows the top selling personal computers in the U.S in 2008 as a percentage of
all personal computers sold. Use it to answer questions 3, 4 and 5.
Dell HP
Acer Apple Other
29% 28% 15% 8%
20%
21. If 6.2 million computers were sold in 2008, how many were in each category? Show your work.
About 1.8 million Dell computers, 1.74 million HPs, .93 million Acers, .5 million Apples, and 1.24 million
Others.
22. In a pie chart of this data, what angle should be used to represent each of the five categories? Show
your work.
Dell’s region is 104.4°, HP’s region is 100.8°, Acer’s region is 54°, Apple’s region is 28.8°, and the Other
region is 72°.
23. Make a pie chart for this data.
Percentage per company
Dell
HP
Acer
Apple
Other
The following table shows the age distribution of Representatives in the US Congress in 2005. Use it
to answer questions 6 and 7.
Under 40
40-49
50-59
60-69
70-79
80 and over
47
151
128
89
12
3
24. How many Representatives were there in the US Congress in 2005? What percentage of them were at
least 70 years old?
There were 430 Representatives. About 3% were at least 70 years old.
25. Draw a histogram of this data.
Representatives in the US Congress
by Age
160
140
120
100
80
60
40
20
0
Representatives in the
US Congress by Age
Under 40-49 50-59 60-69 70-79 80 and
40
over
26. Explain what is meant by a stack plot.
A stack plot is a display of data where each category has its own wedge and the wedges are displayed on
top of one another. The thickness of a wedge indicates the value at that point.
27. Explain what is meant by a multiple bar graph.
A multiple bar graph is very much like a regular bar graph, except that there are two or more bars in each
category.
28. Why is it sometimes difficult to interpret a three dimensional graph?
It is sometimes difficult to interpret a three dimensional graph because there is always some visual
distortion involved when displaying a three dimensional image on a flat page.
29. When is data displayed more clearly on an exponential scale? Give an example.
An exponential scale is used to display data that is growing or shrinking very rapidly, such as bacteria
growth.
30. A recent study has just rated the 5 most popular brands of toothpaste. If you were to display the
findings of this study in a pictograph, what sort of artwork would you use? Be specific.
Tubes of toothpaste could represent the different brands, and toothpaste could be coming out of the
tubes in different lengths depending on the popularity of each brand.
31. Explain what is meant by inflation.
Inflation is the tendency of prices to rise over time.
32. Using only the information in this graph, what can you determine about the real cost of a candy bar
between 1985 and 2005?
Nothing can be determined about the real cost of a candy bar from the given graph because the prices in
the graph are not adjusted for inflation.
33. If you wanted to mislead your readers by making a bar graph, histogram, or line graph appear more
dramatic than perhaps the data indicated, what might you do?
I might start the scale at a higher number than 0 so that it appears more dramatic. On a line graph or
histogram I could also change the sizes of the horizontal scales to make the numbers come out how I
want.
34. What condition constitutes a correlation between two variables?
A correlation exists between two variables when higher values of one variable consistently go with higher
values of another, or when higher values of one variable consistently go with lower values of another.
35. Would you expect a positive correlation, a negative correlation, or no correlation between the
variables years spent in jail and years of education? Explain.
Negative correlation; Those who have spent more time spent in jail will most likely havea lower level of
education.
36. Would you expect a positive correlation, a negative correlation, or no correlation between the
variables size of a real estate development and annual landscaping costs? Explain.
Positive correlation; As the size of a development increases so would the amount of mowing, edging, and
trimming that needs to be done. More chemicals would need to be bought. All of this increases the cost of
landscaping maintenance.
37. Do you think that the following correlation is an example of coincidence, a common cause, or
causality? Whenever the windmill is turning, I hear a rustling noise in the trees.
Common cause
38. Do you think that the following correlation is an example of coincidence, a common cause, or
causality? People who smoke frequently have a higher instance of lung cancer.
Causality
39. Give a physical model for the following cause-and-effect relationship. Since the tax increase, retail
sales have fallen.
The tax increase means that tax payers have less money to spend at retailers, causing the retailers’ sales
to go down.
40. Explain what is meant by cause beyond a reasonable doubt.
A physical model has been identified that is so successful in explaining how one thing causes another
that it seems unreasonable to doubt the causality.
In the following questions, refer to the data given below about average gasoline and diesel prices for
the week of 2/26/06 according to region.
Retail Fuel Prices (per gallon)
Region-Retail Fuel Prices (per gallon)
Gasoline Diesel
East Coast
1.424 1.469
Midwest
1.393 1.428
Gulf Coast
1.375 1.392
Rocky Mountain
1.433 1.504
West Coast
1.608 1.557
Source: Energy Information Administration
41. Draw a scatter diagram for the data. Use the horizontal axis for gasoline prices and the vertical axis
for diesel prices.
Retail Fuel Prices (per gallon)
1.6
1.608, 1.557
1.55
1.433, 1.504
1.424, 1.469
1.5
1.45
Series1
1.393, 1.428
1.375, 1.392
1.4
1.35
1.3
1.4
1.5
1.6
1.7
Gasoline
42. Does a correlation exist between gasoline prices and diesel prices? If so, is it positive or negative?
Yes; positive
43. Is the relationship between gasoline and diesel prices a coincidence, the result of some common
underlying cause, or the result of one of the prices actually being the cause of the other? Explain.
The result of some common underlying cause; Fuel prices differ by region because states have
different air pollution regulations and taxes on fuels, both of which affect the retail price of both
gasoline and diesel. Thus a state with high fuel taxes and expensive pollution standards will
cause higher gasoline and diesel prices in the region.