Statistics and Probability
Review for Chapter 7 and 8 Exam
Name: __________________
Date: ___________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Suppose you were to collect data for the pair of given variables in order to make a scatterplot. Determine for each
variable if it is the explanatory variable, the response variable, or whether it could be both.
1) Studying consistently, high grade point average
1) _______
A) Studying consistently: both
High grade point average: explanatory
B) Studying consistently: both
High grade point average: both
C) Studying consistently: explanatory
High grade point average: both
D) Studying consistently: response
High grade point average: explanatory
E) Studying consistently: explanatory
High grade point average: response
2) Teacher: weekly salary, teacher: years of experience
A) Teacher: weekly salary: both
Teacher: years of experience: explanatory
B) Teacher: weekly salary: explanatory
Teacher: years of experience: response
C) Teacher: weekly salary: response
Teacher: years of experience: explanatory
D) Teacher: weekly salary: both
Teacher: years of experience: both
E) Teacher: weekly salary: explanatory
Teacher: years of experience: both
2) _______
Suppose you are to form a scatterplot by collecting data for the given pair of variables. Determine the likely direction,
form, and strength.
3) Depth, water pressure
3) _______
A) Positive, no form, strong
B) Positive, nonlinear, moderate
C) Negative, nonlinear, moderate
D) Negative, straight, moderate
E) Positive, straight, strong
4) Student: grade point average, student: height (feet)
A) No direction, linear, moderate
B) Negative, straight, moderate
C) No direction, no form, very weak
D) No direction, no form, strong
E) Positive, no form, very weak
4) _______
Find the correlation.
5) Two different tests are designed to measure employee productivity and dexterity. Several
employees are randomly selected and tested with these results.
36
5) _______
75
A) -0.280
B) 0.471
C) 0.115
D) 0.986
E) 0.159
Solve the problem.
6) A science instructor assigns a group of students to investigate the relationship between the pH
of the water of a river and its water's hardness (measured in grains). Some students wrote these
conclusions: "there was a very strong correlation of 1.47 between pH of the water and water's
hardness." Is the calculation of the correlation appropriate?
A) Yes: the pH and the hardness of the water are data collected from the same river.
B) Yes: correlation can be greater than 1.
C) No: there is little or no association.
D) No: correlation must be equal to 1.
E) No: correlation cannot be greater than 1.
6) _______
7) A science instructor assigns a group of students to investigate the linear relationship between
the pH of the water of a river and its water's hardness (measured in grains). Some students
wrote these conclusions: "My correlation of -0.94 shows that there is almost no association
between pH of the water and water's hardness." Is the interpretation of the correlation
appropriate?
A) No: a correlation of -0.94 shows a strong relation in a negative direction.
B) No: correlation is always positive.
C) Yes: pH and hardness of water do not have the same units.
D) Yes: a correlation of -0.94 shows a weak relation in a negative direction.
E) No: the pH and the hardness of the water are data collected from the same river.
7) _______
8) A science instructor assigns a group of students to investigate the relationship between the pH
of the water of a river and its water's hardness (measured in grains). Some students wrote these
8) _______
conclusions: "there was a very strong correlation of 0.917
between pH of the water and
water's hardness." Is the calculation of the correlation appropriate?
A) No: correlation has no units.
B) No: pH and hardness of water have different units.
C) Yes: the pH and the hardness of the water are data collected from the same river.
D) Yes: correlation is less than 1.
E) No: there is little or no association.
Tell what the residual plot indicates about the appropriateness of the linear model that was fit to the data.
9)
9) _______
A) Model is not appropriate. The relationship is nonlinear.
B) Model may not be appropriate. The spread is changing.
C) Model is appropriate.
10)
10) ______
A) Model is appropriate.
B) Model is not appropriate. The relationship is nonlinear.
C) Model may not be appropriate. The spread is changing.
Answer the question appropriately.
11) A random sample of records of electricity usage of homes gives the amount of electricity used
and size (in square feet) of 135 homes. A regression to predict the amount of electricity used (in
kilowatt-hours) from size has an R-squared of 71.8%. The residuals plot indicated that a linear
model is appropriate. Write a sentence summarizing what
says about this regression.
A) Size differences explain 71.8% of the variation in electricity usage.
B) Differences in electricity usage explain 28.2% of the variation in the number of house.
C) Differences in electricity usage explain 71.8% of the variation in the size of house.
D) Size differences explain 71.8% of the variation in the number of homes.
E) Size differences explain 28.2% of the variation in electricity usage.
11) ______
12) The relationship between the number of games won by a minor league baseball team and the
average attendance at their home games is analyzed. A regression to predict the average
12) ______
attendance from the number of games won has an
= 29.9%. The residuals plot indicated that
a linear model is appropriate. What is the correlation between the average attendance and the
number of games won.
A) 0.547
B) 0.837
C) 0.701
D) 0.089
E) 0.299
Use the model to make the appropriate prediction.
13) A random sample of records of electricity usage of homes in the month of July gives the amount
of electricity used and size (in square feet) of 135 homes. A regression was done to predict the
amount of electricity used (in kilowatt-hours) from size. The residuals plot indicated that a linear
13) ______
model is appropriate. The model is
size. How much electricity would you
predict would be used in a house that is 2273 square feet?
A) 3477.6 kilowatt-hours
B) 1363.8 kilowatt-hours
C) 1781.67 kilowatt-hours
D) 159.8 kilowatt-hours
E) 2567.8 kilowatt-hours
Answer the question appropriately.
14) A correlation of zero between two quantitative variables means that
A) re-expressing the data will guarantee a linear association between the two variables.
B) there is no association between the two variables.
C) None of the above.
D) there is no linear association between the two variables.
E) we have done something wrong in our calculation of r.
14) ______
Part II:
For each of the problems please do the following:
A) Write down the line of regression with context
B) Write down the correlation coefficient ( r value) with context
C) Write down the coefficient of determination (r2 )
1)
2)
2) The population of the city of Jackson for the past ten years is listed in the chart below.
a) What is the least square regression equation with context
____________________________________
b) What would the population be of Jackson when it is 60 years
old?________
c) What would the population be of Jackson when it is 100 years old?
____________
d) How old would Jackson be if the population was 27,486.8?
e) What is the slope in context of the problem?
f)
What is the y-intercept in context of the problem?
3.dasdf
The table above shows the years of experience for eight technicians at Lewis Techomatic and the hourly rate of pay each
technician earns.
A) What is the least square regression line?
B) Predict the hourly rate of pay for a person who has 7years of experience.
C) How about for a person who has 12 years experience.
1) E
2) C
3) E
4) C
5) D
6) E
7) A
8) A
9) C
10) B
11) A
12) A
13) E
14) D