Question 1

Use the graph to answer the question.
-The bar graph below shows the relative frequencies of the different blood types. Write a
sentence describing what is revealed by the graph.

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-The...

Question 2

Solve the problem.
-A researcher finds a negative correlation between blood pressure and the number of
vacations that people take. Can you conclude that taking vacations lowers blood
pressure? Propose other explanations for the correlation. Suggest some ways that the
researcher could go about establishing causality. Refer to the six guidelines for establishing
causality.

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-A researcher finds a negative...

Question 3

Answer the question.
-Andrew creates a bar graph to show the increase in his company's sales. He wants to shov the milestones - years in which sales reached 10 million, 20 million, 30 million, 40 million, and 50 million dollars respectively.
The data are shown in the table below:
$\begin{array}{l|c}
\text { Year } & \text { Sales (millions of dollars) } \
\hline 1975 & 10 \
1985 & 20 \
1993 & 30 \
1999 & 40 \
2003 & 50
\end{array}$
 In the graph, Andrew draws 5 equally spaced bars of heights 1 in, 2 in, 3 in, 4 in, and 5 in
respectively. The height of each bar corresponds to the amount of sales. He labels each bar
with the corresponding year (1975, 1985, 1993, 1999, 2003 respectively). Why is the graph
misleading?

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-Andrew creates a bar graph...

Question 4

Answer the question.
-The bar graph below shows the number of car accidents occurring in one city in each of the
years 1993 through 1998. The number of accidents dropped in 1995 after a new speed limit
was imposed. Why is the graph misleading? How would you redesign the graph so that it
is less misleading? What impression is conveyed by the graph?

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The answer of Answer the question.
-The bar graph below shows...

Question 5

Construct the specified histogram.
-30 police detectives were asked how many days they had taken off in the previous year.
The results are summarized in the frequency table below . $$\begin{array} { c | c } 
\text { Days off } & \text { Frequency } \
\hline 0 - 1 & 10 \
2 - 3 & 1 \
4 - 5 & 7 \
6 - 7 & 7 \
8 - 9 & 1 \
10 - 11 & 4
\end{array}$$ Construct a histogram.

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The answer of Construct the specified histogram.
-30 police detectives were...

Question 6

Answer the question.
-The bar graph below shows the average cost of renting a studio in a certain city in each of
the years 1994 through 1998.  By what percentage does the average rental price increase from 1994 to 1995? Obtain a
truncated version of the graph by sliding a piece of paper over the bottom portion of the
graph so that the scale on the vertical axis starts at 300. In the truncated graph, by what
percentage does the price appear to increase from 1994 to 1995? Why is the truncated
graph misleading?

Accepted Answer

The answer of Answer the question.
-The bar graph below shows...

Question 7

Describe how you would apply the five basic steps of a statistical study to the given issue.
-As an executive of a large software company, you want to know whether there has been an
increase in levels of stress amongst your employees.

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Question 8

Make a bar graph to represent the data.
-The following table shows the number of male infants born at Hospital X on New Year's
Day (Jan. 1). Create a horizontal bar graph. $$\begin{array} { c | c } 
& \text { No. of Male } \
\text { Year } & \text { Infants Born on Jan 1 } \
\hline 1990 & 12 \
1991 & 28 \
1992 & 20 \
1993 & 32 \
1994 & 20 \
1995 & 20
\end{array}$$

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Question 9

Use the guidelines to evaluate the study. Discuss flaws that you see in the study.
-An acupuncturist notes that after a month of acupuncture 80% of her patients who had
been suffering from depression are feeling better. The acupuncturist determines the level
of depression by interviewing the patients at the beginning of the month and at the end of
the month. She concludes that acupuncture has an 80% success rate in relieving depression.

Accepted Answer

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Question 10

Describe how you would apply the five basic steps of a statistical study to the given issue.
-You want to know the percentage of college seniors who regret their choice of major.

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Question 11

Create a graphical display for the data given. You may choose any graphic type that you feel is appropriate. Write a fewsentences explaining why you chose this type of display and a few sentences describing any interesting patterns in thedata.
-The table below shows the number of AIDS diagnoses for the United Kingdom by year. $$\begin{array} { c | c | l } 
\text { Year of diagnosis } & \text { Male } & \text { Female } \
\hline 1993 & 1549 & 237 \
1994 & 1628 & 225 \
1995 & 1487 & 282 \
1996 & 1164 & 270 \
1997 & 857 & 216 \
1998 & 592 & 192 \
1999 & 556 & 189 \
2000 & 572 & 236
\end{array}$$

Accepted Answer

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Question 12

Make a bar graph to represent the data.
-The table lists the winners of the Wimbledon women's singles title for the years 1976-1995.
Construct a vertical bar graph for the given relative frequencies. $$\begin{array} { l c c } 
\text { Winner } & \text { Frequency } & \begin{array} { c } 
\text { Relative } \
\text { frequency }
\end{array} \
\hline \text { C. Evert } & 2 & 0.10 \
\text { V. Wade } & 1 & 0.05 \
\text { M. Navratilova } & 9 & 0.45 \
\text { C. Martinez } & 1 & 0.05 \
\text { S. Graf } & 6 & 0.30 \
\text { E. Goolagong } & 1 & 0.05
\end{array}$$

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Question 13

Answer the question.
-A parcel delivery service lowered its prices and finds that it has delivered twice as many
parcels this year as it did last year. To illustrate this fact, the manager draws a pictogram as
shown below. Each cube depicts a parcel. The side length of the "parcel" on the right is
twice the side length of the "parcel" on the left.  Why is this pictogram misleading? What visual impression is portrayed by the pictogram?

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The answer of Answer the question.
-A parcel delivery service lowered...

Question 14

Construct the specified histogram.
-24 high school students were asked how many hours they had spent preparing for a test. The times (in hours) are as follows:
$$6,5,6,4,6,6,9,7,6,3,8,5,5,8,6,5,8,6,5,7,5,8,7,4$$
Use 2 -point bins ( 3 to 4,5 to 6 , etc) to construct the relative frequency histogram.

Accepted Answer

The answer of Construct the specified histogram.
-24 high school students...

Question 15

Solve the problem.
-A researcher suspects that pesticides in foods cause cancer. Suggest some ways that she
could go about establishing causality. Refer to the six guidelines for establishing causality.
For each guideline suggest some research that should be pursued. Discuss any challenges
that the researcher would face in establishing causality.

Accepted Answer

The answer of Solve the problem.
-A researcher suspects that pesticides...

Question 16

Answer the question.
-The mayor of one city has been conducting an anti-smoking campaign in high schools.
Each year local government researchers estimate the number of teenagers in the city who
smoke. The number of smokers has declined steadily in each of the past five years. The
mayor's office constructs a bar graph showing the number of teenage smokers in each of
the past five years. If the mayor wished to exaggerate the success of his anti-smoking
campaign, would it be to his advantage to truncate the bar graph? Explain your thinking.

Accepted Answer

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-The mayor of one city...

Question 17

Use the guidelines to evaluate the study. Discuss flaws that you see in the study.
-A researcher is interested in why Americans have such a high divorce rate. She randomly
selects 100 American married couples and 100 Japanese married couples. She invites each
couple to come into her office and interviews each couple, asking them about their
satisfaction with their marriage.
The researcher also notes that a high percentage of the American women had full time jobs
outside the home, whereas a high percentage of the Japanese women did not have full time
jobs. The researcher concluded that marriages in which the woman has a full time job have
a lower rate of success.

Accepted Answer

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Question 18

Describe how you would apply the five basic steps of a statistical study to the given issue.
-You want to know the average amount paid in rent by tenants of the city of Hazelwood.

Accepted Answer

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Question 19

Use the guidelines to evaluate the study. Discuss flaws that you see in the study.
-The host of a conservative talk show asked his listeners to respond to the following
question: "Do you think that environmental laws which restrict growth should be
weakened?" Twenty people responded, and the next day the talk show host announced
that the results of his survey suggested that 76% of Americans feel that environmental laws
should be weakened.

Accepted Answer

The answer of Use the guidelines to evaluate the study....

Question 20

Use the guidelines to evaluate the study. Discuss flaws that you see in the study.
-A researcher randomly selects 300 adults from the city of Kentwood by using a random
number generator and a list of residents of the town. She calls the people in the sample and
asks the following question: "Do you agree that more of the city's budget should be spent
on social services for the poor? " She announces that 54% of the people in Kentwood feel
that more of the city's budget should be spent on social services for the poor.

Accepted Answer

The answer of Use the guidelines to evaluate the study....

Quiz 5: Statistical Reasoning

Use the graph to answer the question. -The bar graph below shows the relative frequencies of the different blood types. Write a sentence describing what is revealed by the graph.

Describe how you would apply the five basic steps of a statistical study to the given issue. -As an executive of a large software company, you want to know whether there has been an increase in levels of stress amongst your employees.

Describe how you would apply the five basic steps of a statistical study to the given issue. -You want to know the percentage of college seniors who regret their choice of major.

Construct the specified histogram. -24 high school students were asked how many hours they had spent preparing for a test. The times (in hours) are as follows: $6,5,6,4,6,6,9,7,6,3,8,5,5,8,6,5,8,6,5,7,5,8,7,4$ Use 2 -point bins ( 3 to 4,5 to 6 , etc) to construct the relative frequency histogram.

Describe how you would apply the five basic steps of a statistical study to the given issue. -You want to know the average amount paid in rent by tenants of the city of Hazelwood.