MATCHING: For the following problems, write the letter of the most appropriate
statistical analysis technique next to the story. Note: each answer choice may be used
once, more than once, or not at all.
A. Mean and/or
standard deviation
E. Matched pairs
t-test
I. Chi-squared test
B. Simple linear
regression
F. Comparison of
means t-test
J. One-way
ANOVA
C. Multiple
linear regression
G. 1-sample
proportion Z-test
K. Two-way
ANOVA
D. 1-sample mean
t-test
H. 2-sample
proportion Z-test
L. Five number
summary
_____ 1.
Is college major associated with the region of the country a student is from
in the population?
_____ 2.
A group of taste testers is asked to rate (in random order) both Coke and
Pepsi on a scale of 1-10. Is Coke better tasting than Pepsi on average in
the population?
_____ 3.
What is the average taste test rating for Coke on a scale of 1-10 from a
sample of 30 taste testers?
_____ 4.
Do major and region of the country a student is from affect the population
mean GPA?
_____ 5.
Which of the following are important for predicting a student’s graduation
GPA in the population: the number of semesters a student spends in
college, their high school GPA, and their SAT scores?
_____ 6.
Is the population percentage of people in Tippecanoe county who are
Purdue students significantly higher in 2007 than it was in 1994 if a
random sample of residents was taken both years?
_____ 7.
Are height and weight independent in the population?
_____ 8.
Are freshman taller than seniors on average in the population?
_____ 9.
Are population average GPAs the same for science and engineering
majors?
_____ 10.
Are population average GPAs the same for science, engineering, nursing,
and communications majors?
_____ 11.
Is the population average GPA 3.0?
_____ 12.
What is the middle GPA for this sample of students?
1
MATCHING: (3 points each) For problems 1-11, write the letter of the most
appropriate statistical analysis technique next to the story.
Note: each answer choice may be used once, more than once, or not at all.
_____ 1.
Does knowing a college student’s SAT score tell us anything
about his or her first year college GPA in the population?
a.
Mean and/or
standard deviation
_____ 2.
Do college grade point averages differ for male athletes in
football, swimming, and crew in the population?
b.
Five number
summary
_____ 3.
A college instructor wants to know whether the population
average high school GPA for freshman enrolled in college
algebra is below 3.0.
c.
Simple linear
regression
d.
Multiple linear
regression
e.
1-sample mean ttest
f.
Matched pairs t-test
g.
2-sample
(Comparison of
means) t-test
h.
1-sample proportion
Z-test
i.
2-sample proportion
Z-test
j.
Chi-squared test
k.
One-way ANOVA
l.
Two-way ANOVA
_____ 4.
_____ 5.
Does knowing high school seniors’ IQ scores, SAT scores,
and high school GPA tell us anything about their first year
college GPAs in the population?
Do New Mexican high school seniors have higher population
averages than Vermont high school seniors on the national
achievement exam?
_____ 6.
Is college major related to political party affiliation in the
population?
_____ 7.
Do identical twins differ from each other on average in
reading achievement scores in the population?
_____ 8.
_____ 9.
Is support for a school bond issue (Yes or No) higher in the
University Farms than in Chauncey Village neighborhoods?
Is there a difference in population average national
achievement exam scores for seniors from New Mexico,
Florida, and Vermont?
_____ 10.
What is the average national achievement exam score for
200 New Mexico high school seniors?
_____ 11.
Do college major and gender affect the mean GPA for the
population of Purdue students?
2
A. Mean and/or standard B. Simple linear regression
C. Multiple linear regression
deviation
E. Matched pairs t-test F. Comparison of
G. 1-sample
means t-test
proportion Z-test
I. Chi-squared test
J. One-way ANOVA K. Two-way ANOVA
_____ 1.
vacations?
D. 1-sample mean t-test
H. 2-sample proportion
Z-test
L. Five number summary
What is the average amount of money students in this class spend each year on
_____ 2.
Do more than 75% of college students in the population go someplace other than
to their parents’ house for spring break?
_____ 3.
Does the amount of debt a student has increase, on average in the population, if
you compare before and after spring break credit card statements?
_____ 4.
Are g.p.a. and amount of credit card debt independent in the population?
_____ 5.
Is there a difference in average amount of credit card debt if you compare
freshman, sophomores, juniors and seniors in the population of college students?
_____ 6.
What is the range of the middle 50% of my 50 students’ exam scores?
_____ 7.
Is there a relationship between the number of students enrolled in a class and the
average exam score for that class for all the classes at Purdue?
_____ 8.
Do Indiana-born students score higher on average in the population on this test
than students born outside the state?
_____ 9.
Is the population mean of all students taking a national exam different from the 80
that the authors aimed for?
_____ 10. Are political party preference (Democrat, Republican, and Independent) and ice
cream flavor preference related in the population?
_____ 11.
women?
Is the population percentage of unemployed men lower than for unemployed
_____ 12. Are the type of pet you own and your hair color related to your annual salary in
the population?
_____ 13. Is there a population mean difference in preschoolers’ spatial-temporal reasoning
scores after having piano lessons?
_____ 14.
Do higher I.Q. people also have higher college g.p.a.s in the population?
3
_____ 15. Do annual salary, I.Q., and number of children affect a person’s happiness rating
(on a scale of 1-10) in the population?
_____ 16. Do flavor of M&Ms (plain, peanut, and peanut butter) and color
distribution (red, orange, yellow, green, blue, and brown) make a difference to the
population mean taste ratings (scale of 1-10)?
_____ 17. Is there a difference in the population average number of chips in a regular
Chips Ahoy cookie and a reduced-fat cookie?
_____ 18. Is the type of music playing over the speakers in a store associated with
the type of wine a customer buys in the population?
_____ 19. What is the average number of calories in a sample of 20 “fun packs” of
Halloweeen candy?
_____ 20. Does the season (fall, winter, spring, summer) make a difference to
population average pollen counts?
_____ 21. Does the season (fall, winter, spring, summer) and type of trees growing
nearby make a difference to population average pollen counts?
_____ 22. Do the temperature (in degrees), number of trees growing nearby, and %
humidity affect pollen counts in the population?
_____ 23. Do pollen counts decrease on average between noon and midnight on
particular days if a sample of 30 days is used to estimate what is true for the population?
_____ 24.
allergies?
Do at least 30% of the population of Lafayette residents have pollen
_____ 25.
Are gender and type of allergy (pet, dust, pollen) related in the population?
_____ 26. Does increasing the number of ounces of water a person drinks decrease a
person’s calorie consumption on a daily basis in the population?
_____ 27. Does the type of class activity (lab, homework, lecture) used to teach a
concept make a difference to the population average quiz score on that activity?
_____ 28.
What is the minimum score on this exam?
_____ 29. Is the population percentage of students passing this exam higher for
students who did their practice problems than for those who didn’t?
_____ 30. Is the population average number of ounces of water a college student
drinks daily less than the 64 ounces recommended by health experts?
4
So how do you know which is which? Start by deciding whether your variable(s) is/are
categorical or quantitative. The first 2 are statistics, the rest are inference techniques.
Mean and/or standard deviation: just looking for a summary statistic, variable is
quantitative
Five-number summary: Min, Q1, M, Q3, Max, summary statistics for a quantitative
variable
Simple linear regression: using x to predict y, are x and y independent?, x and y are
correlated, as x increases what happens to y, x and y are both quantitative variables
Multiple linear regression: similar to simple linear regression except there will be more
than one x, all variables will be quantitative
1-sample mean t-test: comparing a single mean to a number, each unit is asked a
numerical question (“how many times a week do you ride the bus?”), don’t know the
population standard deviation, quantitative variable
Matched pairs t-test: before and after, left and right, all units are tested twice (a unit
could be a pair of subjects or pair of units) and measurements are compared to each other,
average difference, quantitative variable
Comparison of means t-test: 2 distinct populations with samples chosen independently,
each unit is measured only once, one quantitative variable (your measurement) and one
categorical variable (how you distinguish between your groups, like gender or eye color)
1-sample proportion Z-test: each unit is asked a yes/no question (“did you ride the bus
today?”), proportion comes from taking the # of successes / # of trials, comparing a
proportion or percentage to a number between 0 and 1
2-sample proportion Z-test: similar to 1-sample proportion Z-test except there are 2
distinct populations with samples selected independently so that the proportions can be
compared to each other
Chi-squared test: 2 categorical variables, testing whether there is an association
between the variables
One-way ANOVA: one categorical variable (how you distinguish between your groups)
and one quantitative variable (your measurement), similar to comparison of means t-test
except you can have more than 2 groups to compare
Two-way ANOVA: two categorical variables (how you distinguish between your
groups) and one quantitative variable (your measurement), similar to doing one-way
ANOVA twice except you can also look for the interaction between the two categorical
variables
5