# Chapter 4 Review * Statistics Honors ```Chapter 4 Review – Statistics Honors
Directions:
1.)
Suppose the correlation between two variables x and y is due to the fact that both are responding
to changes in some unobserved third variable. What is this due to?
(a)
(c)
(e)
2.)
cause and effect between x and y
extrapolation
none of the above
(b)
(d)
the effect of the lurking variable
common sense
Suppose a straight line is fit to data having response variable y and explanatory variable x.
Predicting values of y for values x outside the range of observed data is called:
(a)
(d)
3.)
Circle the letter that best answers the question.
correlation
sampling
(b)
(e)
causation
none of the above
(c)
extrapolation
Given the data points below.
x
y
1
5.3
2
7.6
3
11.0
4
16.0
5
24.1
6
33.8
7
43.4
Which of the following transformations to the data will change the scatterplot of the data to a
straight line? *Hint: You must fill in the 4 lists and then look at the different scatterplots to find the most linear
(or look at the r values)
(a)
(c)
(e)
Directions:
4.)
take the log of x and the log of y
take the log of y
none of the above
(b)
(d)
take the log of x
no change is needed
Fill in the blank to best complete each statement.
A two-way table of counts describes the relationship between two ___________________
_______________________.
5.)
_______________________ distributions look at one of the variables in comparison to the entire
table count.
6.)
_______________________ distributions look at either one row or one column as the condition to
the probability.
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Chapter 4 Review – Statistics Honors
Directions:
A researcher suspected a relationship between people preferences in movies and preference in
pizza. A random sample of 100 people produced the following two – way table:
Favorite
Movie
7.)
Show all required work to answer the question.
Pizza Topping Preference
Pepperoni
Ground Beef
Mushrooms
20
5
10
Jurassic Park
Lethal Weapon I
8
15
12
Gone With the Wind
15
2
13
(a)
Enter the counts on the table.
(b)
Find each of the following probabilities, in percents:
(c)
(d)
i.)
P  pepperoni 
iv.)
P(Jurassic ParkMushrooms)
ii.)
P  ground beef 
v.)
What is the marginal distribution of: (in percents)
i.)
Jurasic Park
ii.)
Lethal Weapon I
iii.)
Gone with the wind
What is the conditional distribution of: (in percents)
i.)
Jurasic Park given pepperoni
ii.)
Gone with the wind given ground beef
iii.)
Mushrooms given Lethal Weapon I
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iii.)
P  mushrooms 
P(Ground BeefLethal Weapon I)
Chapter 4 Review – Statistics Honors
* For #8-10, decide if there are any lurking variables that may be impacting the relationship.
Write down what x, y, and z are, draw a diagram of the relationship, and then state whether the
problem represents causation, common response, or confounding. Remember, there are many
8.)
9.)
10.)
Research shows there is a strong positive correlation between ice cream consumption and
murder rates.
(a)
Draw a diagram of the relationship and identify all variables.
(b)
This problem represents causation, common response, or confounding? ____________________
A soccer coach wanted to improve the team's playing ability, so he had them run two miles a day.
At the same time the players decided to take vitamins. In two weeks the team was playing
noticeably better, but the coach and players did not know whether it was from the running or the
vitamins.
(a)
Draw a diagram of the relationship and identify all variables.
(b)
This problem represents causation, common response, or confounding? ____________________
Over the past 30 years in the United States there has been a strong positive correlation between
cigarette sales and the number of high school graduates.
(a)
Draw a diagram of the relationship and identify all variables.
(b)
This problem represents causation, common response, or confounding? ____________________
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Chapter 4 Review – Statistics Honors
11.)
George was doing a science experiment and determined that the population of fruit flies is
described by the equation: log( population )  2.6  .02( time in days )
Based on this equation, what is the approximate population of fruit flies in 30 days? Hint: You will
have to rearrange the given equation to “get rid of” the log.
12.)
The number of motor vehicles registered (in millions) in the U.S has grown as follows:
Year (x)
Vehicles (y)
Year
Vehicles
1940
1945
1950
1955
1960
32.4
31.0
49.2
62.7
73.9
1965
1970
1975
1980
1985
90.4
108.4
132.9
155.8
171.7
(a) Plot the number of vehicles against time on your calculator (don’t forget to change the years to year #).
Assume the curved growth pattern exhibited is exponential.
(b) Write the transformed LSRL and then use inverse transformations to transform the equation into an
exponential equation.
13.)
A curious thing happened to two baseball players this year during the first two weeks of the
season. Here are the data :
Weekly Results
Week
1
2
At bats
5
20
Player 1
Hits
2
5
Batting Avg.
At bats
25
5
Player 2
Hits
9
1
Batting Avg.
(a)
Show that each week, Player 1 had a higher batting average than does Player 2. (Fill in table above)
(b)
Show that at the end of the two weeks, the cumulative results for Player 2 were better than the
cumulative results for Player 1.
(c)
What is the name for this apparent contradiction? ___________________________________
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