STATISICS

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MGF1106
Unit Five Ex. 7.3 Inferring Relations And Making
Accurate Predictions From Studying Statistical
Data Objective 4
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Exercise 7.3
Objective 4
To infer and make accurate predictions from
studying statistical data
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A positive relationship exists between two
variables if an increase in one variable produces
an increase in the other variable.
Example One would expect a positive relationship
between the number of shirts bought and the cost
of these shirts.
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A positive relationship could be shown between
some past annual mean salaries for teachers in a
school system and the annual per capita liquor
consumption (in gallons) for Americans.
Warning!
We cannot establish the existence of a
cause-and-effect relationship! This does not
imply that teachers are using their raises to buy
more liquor!
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The number at bat and the batting average of ten
boys are given in the table below.
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A. Increasing the number at bat caused an
increase in the batting average.
B. Increased batting average caused the boy to
get more at bats.
C. There appears to be a positive association
between the number at bats and the batting
average.
D. The number at bat does not provide
information needed to predict the batting
average.
C
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Consider the following plot of the number of
customers browsing in the junior sportswear
department of a major clothing store and the
amount of sales for the department.
Customers Browsing
Sales
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Which of the following best describes the trend
in sales?
A. There is no apparent association between
sales and the number browsing.
B. Increased number of people browsing caused an
increase in sales.

• There is an association between the number
  browsing and the amount of sales.

D. There is an association between the number of
people browsing and the amount of sales.
C
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Using the figure given in the previous problem ,
which of the following best estimates the number
of people browsing that would product 200 in
sales?
A. 20 B. 26 C. 28 D. 30
D
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Consider the following graph of the best hitter
in a youth baseball league.
Hits for 8 years (1984 - 1991)
Hits
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In what year did the number of hits begin to
stabilize? _____
1989
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Number of Graduates
Year
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A. The number of graduates tend to level off
for the boys in the late 1980s.
B. The number of graduates tend to increase for
the boys in the late 1990s while the number of
graduates for the girls began to show a decrease.
C. The number of graduates tend to increase for
the girls over the years described.
D. The number of graduates tend to decrease for
the boys over the years described.
B
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The next graph depicts the scores on the midterm
exam and score on the final exam for boys( )
and girls( ).

• A relationship between the final exam and
  midterm exam exists only for boys.

B. A relationship between the final exam and
midterm exam exists only for girls.
C. Students scoring higher on midterm exams tend
to score higher on final exams a stronger
relationship exists for boys than for girls.
D. Students scoring higher on midterm exams tend
to score higher on final exams a stronger
relationship exists for girls than for boys.
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Final Scores
Midterm Scores
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The next graph depicts the scores on the midterm
exam and score on the final exam for boys( )
and girls( ).

• A relationship between the final exam and
  midterm exam exists only for boys.

B. A relationship between the final exam and
midterm exam exists only for girls.
C. Students scoring higher on midterm exams tend
to score higher on final exams a stronger
relationship exists for boys than for girls.
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D. Students scoring higher on midterm exams tend
to score higher on final exams a stronger
relationship exists for girls than for boys.
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Hint Draw an oval around the red points and draw
a oval around the yellow points. The stronger
relationship exists for the more cigar-shaped
oval! In this case it was the red oval.
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Final Scores
Midterm Scores