Sample of CollegeLevel Math Attributes in Statistics
Prepared by: John Climent
Typical Course Description:
This course introduces the students to the study of measures of central tendency, measures of variation, graphical representation of data, least squares regression, correlation, probability, probability distributions, sampling techniques, parameter estimation and hypothesis testing. The use of technology is integrated throughout the course. The emphasis is on applications from a variety of sources including newspapers, periodicals, journals and many of the disciplines that students may encounter in their college education. Students shall be expected to gather and analyze data, and formally report the results of their research.
Typical Outcomes:
Students
successfully completing this course should be able to:
A. Understand the terminology used in statistics.
B. Understand the formulas used in statistics and be able to perform calculations using them.
C. Summarize data both graphically and in tables.
D. Fit least squares regression to data and understand the meaning of the terminology, measures and calculations used in regression.
E. Perform elementary probability calculations, and solve problems using standard probability distributions (e.g., discrete, binomial, uniform and normal).
F. Understand the sampling distribution of the mean and the central limit theorem.
G. Solve problems involving confidence intervals and parameter estimation.
H. Solve problems involving single sample hypothesis tests.
Several of the following may also be required:
I. Solve problems involving twosample hypothesis tests and confidence intervals.
J. Solve problems involving oneway ANOVA.
K. Solve problems involving nonparametric tests.
Attributes 
Sample Problems from CollegeLevel Statistics 
Prerequisite Problems or Skills from Intermediate Algebra 
1, 2, 3, 4, 5, & 6. 
1. An
economist wishes to estimate a line, which relates personal consumption expenditures
(C) and disposable income (I). Both C
and I are in thousands of dollars. She
interviews 8 heads of households for families of size four and obtains the
following data: C 16 18
13 21 27
26 36 39 I 20 20 18
27 36 37
45 50 Let I represent the
independent variable. a.
Use a
graphing utility to draw a scatter plot. b.
Use a
graphing utility to fit a straight line to the data. c.
Interpret
the slope. The slope of this line is
called the marginal propensity to
Income. d.
Predict the
consumption of a family whose disposable income is $42,000. e.
Predict the
disposable income of a family whose consumption is $30,000. f.
What is the
level of measurement for these two variables? g.
Explain
whether or not a linear model is advisable for this data. h.
How strong
is the relationship between these two variables? Cite specific measures. i.
What
percent of the variation is explained by the regression equation? 
1. Each
Sunday, a newspaper agency sells x copies of a certain newspaper for $1.00
per copy. The cost to the agency of
each newspaper is $0.50. The agency
pays a fixed cost for storage, delivery, and so on of $100 per Sunday. a.
a. Write
the equation that relates the profit P, in dollars, to the number x of copies
sold. b.
Graph your
equation. c.
What is the
profit to the company, if 5000 copies are sold? d.
How many
copies must the company sell to make a profit of $5000? e.
Find the
slope of the equation and give a one or two sentence narrative interpreting
it within the context of this problem. Intermediate Algebra Skills Needed: Linear equations, solving linear equations for the dependent variable, graphing lines and points, slope, etc. 
1, 2, 3, 4, 5, & 6. 
2. The
following data comes from an Time of Day 9,10,11,12,13,14,15,16 Minutes to Redden34,20,15,13,14,18,32,60 We are trying to see
if there is a relationship between Time of Day and Minutes to Redden. a.
What is the
explanatory variable and what is its level of measurement? b.
What is the
response variable and what is its level of measurement? c.
Use a
graphing utility to draw a scatter plot. d.
Use a
graphing utility to find the curve of best fit for this data. e.
Draw a
scatter plot of this data along with the curve of best fit. f.
What is the
mathematical name for the curve that best fits this data? g.
Explain why
the correlation coefficient should not be used with this data. h.
Based on
the equation of best fit, how much time can you spend in the sun at i.
If you
needed to spend 20 minutes in the sun, based on your equation of best fit,
for what interval(s) during the day would could you safely spend in the sun
before reddening? j.
How strong
is the relationship between these two variables? Cite specific measures. k.
What
percent of the variation is explained by the regression equation? 
2. The height
H, in feet, of a projectile with an initial velocity of 96 ft./sec launched
from 120 ft. above ground level is given by the equation _{}, where t = time in seconds. Sketch the graph of this function and find
the following. a.
How many
seconds after the launch is the projectile 128 ft. above the ground? b.
What is the
projectile’s maximum height and when does it reach that height? c.
How many
seconds after the launch does the projectile return to the ground? Intermediate Algebra Skills Needed: Parabolas, graphing nonlinear functions, solving quadratic equations, etc. 
1,
2, 3, 4, 5, & 6. 
3 The
data shown in the scatter plot below represents the prices of used Honda
Accords collected from two separate newspapers in 1999. The data itself can be found on the
computer file HondaSpring99. We are trying to see
if there is a relationship between Price and Year. a.
What is the
explanatory variable and what is its level of measurement? b.
What is the
response variable and what is its level of measurement? c.
Explain why
linear, quadratic or cubic relationships are not the appropriate for this
data. d.
Use a
graphing utility to find the curve of best fit for this data. e.
Draw a
scatter plot of this data along with the curve of best fit. f.
What is the
mathematical name for the curve that best fits this data? g.
Explain why
the correlation coefficient should not be used with this data. h.
Based on the
equation of best fit, what should you expect to pay for a 1984 Honda Accord? i.
If you
could only spend $8,000 (not one penny more), based on your equation of best
fit, what was the latest model Honda Accord you could expect to purchase? j.
How strong
is the relationship between these two variables? Cite specific measures. k.
What
percent of the variation is explained by the regression equation? l.
Fit a
linear, quadratic, cubic and exponential equation to this data. Summarize the following results in a table:
mathematical model, regression equation, coefficient of determination,
expected price of a 1992 Honda Accord, expected price of a 1980 Honda
Accord. Use the information from this
table to explain why the exponential model is the recommended model, even
though some of the other models have a higher value for R^{2}. 
3. A model
for the number of people N in a community college who have heard a certain
rumor is _{}, where P is the total population of the community college
and d is the number of days that have elapsed since the rumor began. In a community of 1000 students, find the
following: a.
How many
students will have heard the rumor after 3 days? b.
How many
days will have elapsed before 450 students have heard the rumor? Intermediate Algebra Skills Needed: Finding, graphing and determining exponential functions, using logarithms as an inverse to exponential functions, etc. 
1, 2, 3, 4, 5, & 6. 
4. We wish to determine whether grade point
averages (GPA) differ for boys and girls.
It is assumed that the GPA is normally distributed with an identical
variance for both sexes. Two
independent samples of five students each yield the observations listed
below. Using a 0.05 level of
significance, test whether or not the mean GPA for boys is the same as the
mean GPA for girls. GPA for boys: 2.7
2.9 2.5 3.2
2.8 GPA for
girls: 3.4 2.6
2.6
3.0 3.3. Note: The student will have to use the formula _{}. 
4. Intermediate Algebra Skills Needed: Here it is hard to pinpoint a specific problem from Intermediate Algebra that compares directly with this problem. Clearly one needs to be familiar with nontrivial algebraic formulas and be able to use substitution to evaluate them. The student should recognize the reasonableness of the answer obtained. In addition, the problem given requires higherlevel problem solving skills that those typically found in Intermediate Algebra. 
1, 2, 3, 4, & 5. 
5a. Consider
the Uniform Distribution: _{}, find its mean and standard deviation, and find the
following probabilities: _{}. 5b. If 80% of all 
5. Intermediate Algebra Skills Needed: Both of these problems require a familiarity with function notation. The first problem requires graphing a problem with a limited domain and finding areas of geometric figures. The second problem requires higherlevel problem solving skills than Intermediate Algebra. The student must first recognize that this is a binomial probability problem. Knowledge of factorials and binomial coefficients is also required (usually taught in Statistics). 
1, & 2. 
6. For
the following boxplots, histograms, stemandleaf
diagrams and density functions (not
shown here) describe their shape
(symmetric, skewed right, or skewed left).
For those that are symmetric, give their axis of symmetry. In addition, comment on the variability of
the various distributions. 
6. Intermediate Algebra Skills Needed: Knowledge of families of functions, such as, _{}are needed. As is the concept of symmetry. 
3. 
7. Solve
the following inequality for μ: _{}. 
7. Intermediate Algebra Skills Needed: Solving inequalities and literal equations is needed, along with manipulating rational expressions. 
1, 2, & 3. 
8. A bank has 244 customers with balances from $0 to over $15,000. Two of their customers are listed in the
table below. Customer Balance Percentile ZScore Jan $1,150 24 1,50 Mark $8,000 55 0.45 a. Which
customer has a balance that is closest to the mean? b. To
the nearest whole number, calculate the approximate number of customers with
balance below $8,000. c. To
the nearest whole number, calculate the standard deviation for this data. 
8. Intermediate Algebra Skills Needed: Setting up and solving two equations and two unknowns. 
1, 2, 3, 4, 5, & 6. 
9. We
often look at time series data to see the effect of a social change or new
policy. Here are data on motor vehicle
deaths in the Year Rate
Year Rate Year
Rate Year Rate 1960 5.1
1968 5.2 1976
3.3 1984 2.6 1962 5.1
1970 4.7 1978
3.3 1986 2.5 1964 5.4
1972 4.3 1980
3.3 1988 2.4 1966 5.5 1974
3.5 1982 2.8
1990 2.2 a. What
is the level of measurement for Rate? b. What
is the level of measurement for Year? c. Is
this study observational or experimental? d. Draw
a linetype time series plot (not
a bar chart type) of this death rate data and describe the overall pattern of
this data (how it varies over time).
Use year as the independent variable and label your axes. e. In
1974 the national speed limit was lowered to 55 miles per hour in an attempt
to conserve gasoline after the 1973 Mideast war. In the mid1980s most states raised speed
limits on interstate highways to 65 miles per hour. Some said that the lower
speed limit saved lives. Explain if
the effects of the lower speed limits between 1974 and the mid1980s are
visible in your plot. 
9. Intermediate Algebra Skills Needed: Choosing and labeling axes, plotting points, drawing lines and familiarity with a variety of graphs. 
1, 2, 3, & 5. 
10. If P(A) =
0.4, P(B) = 0.2 and P(AB) = 0.5, find the following: P(AÇB), P(BA),
and P(AÈB). What must we change the value of P(A) to, in order to make events A and B independent events? 
10. Intermediate Algebra Skills Needed: Familiarity with function notation, solving literal equations, and substitution. 
1, 2, 3, 4, 5, & 6. 
11. Jim and Yvette plan to have a family of three
children, with girls being just as likely as boys. Find the probability distribution for the
number of girls and the probability that all of their children are boys. 
11. Intermediate Algebra Skills Needed: Familiarity with function notation, substitution, and higherorder problem solving skills. 
1, 3, & 5. 
12. Find the mean, variance and standard
deviation for the probability distribution given: X 1 2 3 4P(X) .1 .3
.2 .3

12. Intermediate Algebra Skills Needed: Familiarity with function notation, and substitution in
complex algebraic formulas. 
1, 2, 3, 4, 5, & 6. 
13. With increased airline traffic, it is
predicted that in the next century airline accidents will average one a
week. If they follow a Poisson
distribution, what is the probability that the number of airline accidents in
a month (4.3 weeks) is at least 7? In
addition, find the mean, variance and standard deviation. 
13. Intermediate Algebra Skills Needed: Familiarity with function notation, substitution in
complex algebraic formulas, exponential functions and higherlevel problem
solving skills. 
1, 2, 3, 4, 5, & 6. 
14. A police officer buys a box of 13 jelly
donuts (a baker's dozen). Nine of the donuts are strawberry and four are
raspberry. If the police officer
randomly selects and eats 5 of the donuts, what is the probability that he or
she eats at least 2 strawberry jelly donuts?
In addition, find the mean, variance and standard deviation. 
14. Intermediate Algebra Skills Needed: Familiarity with function notation, substitution in
complex algebraic formulas and higherlevel problem solving skills. 
1, 2, 3, 4, 5, & 6. 
15. Suppose that of all students, who took a standardized
math test, their average score was 980 with a standard deviation of 100. If test scores are normally distributed,

15. Intermediate Algebra Skills Needed: Using formulas and tables, substitution, and higherlevel problem solving skills. 
1, 2, 3, 4, 5, & 6. 
16. Janice wanted to estimate mean number of
hours her dog spent sleeping each day.
In sample of 29 days, she found that her dog slept for an average of
18.7 hours with a standard deviation of 4.7 hours.

16. Intermediate Algebra Skills Needed: Familiarity with function notation, substitution in
complex algebraic formulas, using and solving inequalities, using tables, and
higherlevel problem solving skills. 
1, 2, 3, 4, 5, & 6. 
17. The Associated Press reported that in a
recent survey of 8000 women, 648 said that they were stalked at least
once. Stalking was defined by
researchers as: “a course of conduct directed at a specific person that
involves repeated physical or visual proximity, nonconsensual communication,
or verbal, written or implied threats.”

17. Intermediate Algebra Skills Needed: Familiarity with function notation, substitution in
complex algebraic formulas, using and solving inequalities, using tables, and
higherlevel problem solving skills. 
1, 2, 3, 4, 5, & 6. 
18. In a recent survey, it was discovered that 14
out of 50 people owned subcompact cars.
In a related survey, it was found that 18 out of 100 people owned
luxury cars. Can we conclude at a 0.05
significance level that subcompact cars are more popular than luxury cars? 
18. Intermediate Algebra Skills Needed: Using formulas and tables, substitution, and higherlevel
problem solving skills. 
1, 2, 3, & 5. 
19. Suppose that we are testing H_{0}: m = 45 and it is appropriate to use
the ztest. If the value of our statistical formula is z = 1.23, find the pvalue that corresponds to the
following possible alternative hypotheses: H_{1}: m > 45, H_{1}: m < 45 and H_{1}:
m ¹ 45. 
19. Intermediate Algebra Skills Needed: Using formulas and tables, substitution, and higherlevel
problem solving skills. 
1, 2, 3, 4, 5, & 6. 
20. A test is normally distributed with a mean
of 64.3 and a standard deviation of 7.2.
Find the highest B if the top 10% of the students receive an A. 
20. Intermediate Algebra Skills Needed: Using formulas and tables, substitution, inverse functions, and higherlevel problem solving skills. 