Exercises
Which type of data (categorical, discrete
numerical, continuous numerical) is each of the
following variables?
a. Age of a randomly chosen tennis player in the
Wimbledon tennis tournament.
b. Nationality of a randomly chosen tennis player in
the Wimbledon tennis tournament.
c. Number of double faults in a randomly chosen
tennis game at Wimbledon.
Which measurement level (nominal, ordinal,
interval, ratio) is each of the following variables?
a. A customer’s ranking of fi ve new hybrid
vehicles.
b. Noise level 100 meters from the Dan Ryan
Expressway at a randomly chosen moment.
c. Number of occupants in a randomly chosen
commuter vehicle on the San Diego Freeway.
There are 327 official ports of entry in the United
States. The Department of Homeland Security
selects 15 ports of entry at random to be audited
for compliance with screening procedures of
incoming travelers through the primary and
secondary vehicle and pedestrian lanes. What
kind of sample is this (simple random, systematic,
stratifi ed, cluster)?
The durations (minutes) of 26 electric power
outages in the community of Sonando Heights
over the past five years are shown below.
(a) Duration Prepare a stem-and-leaf plot.
(b) Prepare a dot plot.
(c) Prepare a frequency distribution and
histogram.
(d) Describe the distribution, based on these
displays.
Data file: Duration
Revenue and Net Income (millions) for 27 Randomly
Chosen Fortune 1000 Companies.
(a) Use Excel to make a scatter plot, placing Revenue
on the X-axis and Net Income on the Y-axis. Add
titles and modify the default colors, fonts, etc., as
you judge appropriate to make the scatter plot
effective.
(b) Describe the relationship (if any) between X and Y.
Weak? Strong? Negative? Positive? Linear?
Nonlinear?
Data file: RevenueIncome
The table below shows average daily sales of Rice
Krispies in the month of June in 74 Noodles &
Company restaurants.
(a) Make a histogram for the data.
(b) Would you say the distribution is skewed?
(c) Calculate the mean and standard deviation.
(d) Are there any outliers?
Data file: RiceKrispies
Analysis of annualized returns over a 10-year
period showed that prepaid tuition plans had a
mean return of 6.3 percent with a standard
deviation of 2.7 percent, while the Standard &
Poor’s 500 stock index had a mean return of 12.9
percent with a standard deviation of 15.8 percent.
(a) Calculate and compare the coefficients of
variation.
(b) Why would we use a coefficient of variation?
Why not just compare the standard deviations?
Analysis of annualized returns over a 10-year
period showed that prepaid tuition plans had a
mean return of 6.3 percent with a standard
deviation of 2.7 percent, while the Standard &
Poor’s 500 stock index had a mean return of 12.9
percent with a standard deviation of 15.8 percent.
(a) Calculate and compare the coefficients of
variation.
(b) Why would we use a coefficient of variation?
Why not just compare the standard deviations?
The contingency table below shows the results of a survey of
online video viewing by age. Find the following probabilities or
percentages:
a. Probability that a viewer is aged 18–34.
b. Probability that a viewer prefers watching TV videos.
c. Percentage of viewers who are 18–34 and prefer watching
user-created videos.
d. Percentage of viewers aged 18–34 who prefer watching
user-created videos.
e. Percentage of viewers who are 35–54 or prefer user
created-videos.
In the last 50 years, the average number of deaths
due to alligators in Florida is 0.3 death per year.
Assuming no change in this average, in a given
year find the probability of
(a) no alligator deaths;
(b) (b) at least 2 alligator deaths.
The diameter of bushings turned out by a
manufacturing process is a normally distributed
random variable with a mean of 4.035 mm and a
standard deviation of 0.005 mm. A sample of 25
bushings is taken once an hour.
(a) Within what interval should 95 percent of the
b ushing diameters fall?
(b) Within what interval should 95 percent of the
sample means fall?
(c) What conclusion would you reach if you saw a
sample mean of 4.020? A sample mean of
4.055?
A poll of 125 college students who watch The Big
Bang Theory showed that 83 of them usually
watch on a mobile device (e.g., laptop).
(a) Assuming that this was a random sample,
construct a 90 percent confidence interval for
the proportion of all college students who
usually watch this show on a mobile device.
(b) Would a finite population correction be
required? Explain.
To encourage telephone efficiency, a catalog call
center issues a guideline that at least half of all
telephone orders should be completed within 2
minutes. Subsequently, a random sample of 64
telephone calls showed that only 24 calls lasted 2
minutes or less.
(a) At α 5 .05 is this a significant departure from
the guideline in a left-tailed test? State your
hypotheses and decision rule.
(b) Find the p-value.
An experimental surgical procedure is being studied
as an alternative to the old method. Both methods
are considered safe. Five surgeons perform the
operation on two patients matched by age, sex, and
other relevant factors, with the results shown. The
time to complete the surgery (in minutes) is recorded.
(a) At the 5 percent significance level, is the new way
faster? State your hypotheses and show all steps
clearly.
(b) Is the decision close?
Data file: Surgery
In 2006, a sample of 200 in-store shoppers
showed that 42 paid by debit card. In 2009, a
sample of the same size showed that 62 paid by
debit card.
(a) Formulate appropriate hypotheses to test
whether the percentage of debit card
shoppers increased.
(b) Carry out the test at α 5 .01.
(c) Find the p-value.
The XYZ Corporation is interested in possible
differences in days worked by salaried employees
in three departments in the financial area. A
survey of 23 randomly chosen employees reveals
the data shown below. Because of the casual
sampling methodology in this survey, the sample
sizes are unequal.
Research question: Are the mean annual
attendance rates the same for employees in these
three departments?
Data file: DaysWorked
Several friends go bowling several times per month. They keep
track of their scores over several months. An ANOVA was
performed.
(a) What kind of ANOVA is this (one-factor, two-factor, etc.)?
(b) How many friends were there? How many months were
observed? How many observations per bowler per month?
Explain how you know.
(c) At α 5 .01, what are your conclusions about bowling scores?
Explain, referring either to the F tests or p-values.
In the following regression, X = weekly pay, Y = income
tax withheld, and n = 35 McDonald’s employees.
(a) Write the fitted regression equation.
(b) State the degrees of freedom for a two-tailed test
for zero slope, and use Appendix D to find the
critical value at α 5 .05.
(c) What is your conclusion about the slope?
(d) Interpret the 95 percent confidence limits for the
slope.
(e) Verify that F = t2 for the slope.
(f) In your own words, describe the fit of this
regression.