Business statistics are statistics applied to the business world in an effort to improve
people’s decision making in fields such as marketing research, operations, finance, and
advertising.
When creating a frequency distribution with grouped qualitative data and 45 data
points, five classes should be set up using the 2k > n rule.
Analysis of variance is a technique used to conduct a hypothesis test to compare three
or more population proportions simultaneously.
As the sample size increases, the interval that contains 95% of the sample means
becomes narrower.
The sample correlation coefficient can be a positive value, a negative value, or zero.
If there were no difference in the population medians for the Kruskal-Wallis test, we
would expect the average ranks of all of the samples to be fairly close to one another.
The Wilcoxon rank-sum test is a nonparametric procedure that determines whether two
populations have the same probability distribution based on evidence from two
independent samples.
A 99% confidence interval has a greater chance of “catching” the true population mean
when compared to a 90% confidence interval.
The finite population correction factor for adjusting the confidence interval when
sampling from a finite population is used when .
If the occurrence of one event affects the occurrence of another event, the events are
considered mutually exclusive.
Prior probabilities are a revision of posterior probabilities using additional information
such as the results of a market survey.
If the population does not follow the normal probability distribution, the Central Limit
Theorem tells us that the sample means will be normally distributed with sufficiently
large sample size. In most cases, sample sizes of 5 or more will result in sample means
being normally distributed, regardless of the shape of the population distribution.
A Type II error is known as the producer’s risk because, when it occurs in quality
control settings, the producer is looking for a problem in its process that does not exist.
Histograms displaying discrete data usually have gaps between their bars.
When using the index point, i, to determine the pth percentile of a data set, round i to the
next whole number, if is not a whole number.
The purpose of Bayes’ Theorem is to update prior probabilities based on information
provided by posterior probabilities.
The goal is for the Cp statistic to be less than or equal to k + 1, where k equals the
number of independent variables.
The Durbin-Watson statistic isused to test for the presence of autocorrelation in a series
of residuals.
A scatter plot is a useful tool to examine the data before conducting correlation analysis.
Trend projectionis a forecasting technique that projects into the future a linear
regression equation that best fits the data in a time series.
The convention for weighted moving average forecasting is to assign the lowest weight
to the most recent data and the highest weight to the oldest data with the reasoning that
the most recent data is more relevant.
The shape of the exponential distribution is completely described by only one
parameter, μ.
One-way ANOVA uses a one-tail hypothesis test while two-way ANOVA uses a two-tail
hypothesis test.
The null hypothesis for a chi-square goodness-of-fit test always states that the stated
distribution is followed.
If two variables have a correlation coefficient equal to +0.70 from a sample size of 9,
we can conclude that the population correlation coefficient is greater than zero using α
= 0.05.
When the population slope is equal to zero, there is a relationship between the
dependent and independent variables.
Joint probability is another term used for simple probability.
To help ensure good questionnaire design, it is recommended that a survey is tested on a
small group of respondents before releasing it to the actual participants.
Replications represent the number of data values assigned to each cell in a randomized
block ANOVA table.
The smaller the test statistic for the Wilcoxon signed-rank test, the more likely that we
will be able to reject the null hypothesis.
An expected value is another term for the mean of a probability distribution.
The purpose of generating a confidence interval for the mean is to provide an estimate
for the value of the population mean.
When determining the sample size required for a 95% confidence interval for the
population mean, the sample mean needs to be known.
Discrete random variables have outcomes that typically take on whole numbers as a
result of conducting an experiment.
Using the maximin criterion you identify the best payoff for each alternative and then
choose the alternative that is the “worst of the best”.
The median of a data set is found by adding all the values in the data set and then
dividing the result by the number of observations.
If two variables have a correlation coefficient equal to +0.75, the scatter plot will have
an upward slope moving from left to right.
Residual values in a regression model can be positive or negative.
The degrees of freedom for the total sum of squares for one-way ANOVA equal the
total number of observations minus two.
The following frequency distribution displays the daily sales of muffins at Avalon
Bakery.
What is the probability that between 15 to 21 muffins will be sold tomorrow?
A) 0.26
B) 0.36
C) 0.44
D) 0.50
Use the information below to answer the following question(s).
Cape May Realty manages rental beach properties during the summer season for
property owners. They would like to determine if a relationship exists between the
square footage of beach property and the weekly rental rates during the summer season.
Simple regression analysis was performed using a random sample of beach properties
with the results shown below.
Which one of the following statements is true using α = 0.05?
A) Because the 95% confidence interval for the population slope includes zero, we can
reject the null hypothesis and conclude that there is a relationship between the weekly
rental and square footage of beach property.
B) Because the 95% confidence interval for the population slope includes zero, we fail
to reject the null hypothesis and conclude that there is no relationship between the
weekly rental and square footage of beach property.
C) Because the 95% confidence interval for the population slope does not include zero,
we can reject the null hypothesis and conclude that there is a relationship between the
weekly rental and square footage of beach property.
D) Because the 95% confidence interval for the population slope does not include zero,
we fail to reject the null hypothesis and conclude that there is no relationship between
the weekly rental and square footage of beach property.
Consumer Reports would like to conduct a hypothesis test to determine if the average
battery life for an iPad is different from the average battery life for a Kindle Fire. The
following data represents the battery life from a random sample of iPads and Kindle
Fires in hours. Assume that the population variances are equal.
Define Population 1 as iPads and Population 2 as Kindles. Construct a 98% confidence
interval for the difference in population mean and interpret the results.
Lisa is a regional manager for a restaurant chain that has locations in the towns of
Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in
the proportion of customers who rate their experience as satisfactory or better between
the three locations. The following data represent the number of customers who
indicated they were satisfied from random samples taken at each location.
The expected frequency of satisfied customers from the Berwick sample is ________.
A) 60
B) 75
C) 80
D) 90
Dr. Jordan operates a dental practice with 315 patients and she would like to estimate
the proportion of her patients that have dental insurance from their employers. A
random sample of 110 patients found that 40 had insurance coverage. The 95%
confidence interval to estimate the proportion of patients with dental insurance is
________.
A) (0.227, 0.501)
B) (0.291, 0.437)
C) (0.327, 0.401)
D) (0.346, 0.383)
Sony would like to test the hypothesis that the average age of a PlayStation user is
different from the average age of an Xbox user. A random sample of 36 PlayStation
users had an average age of 34.2 years while a random sample of 30 Xbox users had an
average age of 32.7 years. Assume that the population standard deviation for the age of
PlayStation and Xbox users is 3.9 and 4.0 years, respectively. Sony would like to set α
= 0.10. Which one of the following statements is true?
A) Because the p-value is greater than α, we fail to reject the null hypothesis and can
conclude that the average age of PlayStation users is different from the average age of
Xbox users.
B) Because the p-value is greater than α, we fail to reject the null hypothesis and cannot
conclude that the average age of PlayStation users is different from the average age of
Xbox users.
C) Because the p-value is less than α, we fail to reject the null hypothesis and conclude
that the average age of PlayStation users is equal to the average age of Xbox users.
D) Because the p-value is less than α, we reject the null hypothesis and can conclude
that the average age of PlayStation users is different from the average age of Xbox
users.
The ________ measures the total variation in the dependent variable in multiple
regression.
A) sum of squares within
B) sum of squares error
C) sum of squares regression
D) total sum of squares
If a customer at a particular grocery store uses coupons, there is a 50% probability that
the customer will pay with a debit card. Thirty percent of customers use coupons and
35% of customers pay with debit cards. Given that a customer pays with a debit card,
the probability that the same customer uses coupons is ________.
A) 0.22
B) 0.43
C) 0.60
D) 0.72
Use the following information to answer the question(s) below.
The National Football League has developed a regression model to predict the number
of wins during a season for a team using the following independent variables:
•Average points per game during the season (PPG)
•Average number of penalties committed per game during the season (PEN)
•Turnover differential during the season (TO)
Turnover differential is defined as the number of times the team took the ball away from
their opponent with a turnover minus the number of times the team gave the ball away to
their opponent with a turnover. For example, if TO = +5, the team had five more
takeaways than giveaways. If TO = “7, the team had seven more giveaways than
takeaways during the season.
The following Excel output shows the partially completed regression output from a
random season.
The test statistic for testing the significance of the PPG variable is ________.
A) 0.40
B) 3.90
C) 4.60
D) 5.19
Using the _____________ criterion you identify the worst payoff for each alternative
and then choose the alternative that is the “best of the worst”.
A) Hurwicz
B) equally likely
C) maximin
D) maximax
There are 23 golfers participating in a weekend tournament. Prizes are awarded to the
first, second, third, and fourth place finishers. The number of different ways these four
places can be filled by those playing over the weekend is ________.
A) 3,450
B) 8,855
C) 70,256
D) 212,520
The Centers for Disease Control (CDC) would like to test the hypothesis that the
proportion of obese adults in the U.S. has increased this year when compared to last
year. A random sample of 125 adults this year found that 56 were obese. Last year, a
random sample of 140 adults found that 42 were obese. If Population 1 is defined as
this year and Population 2 is defined as last year, the p-value for this hypothesis test is
________.
A) 0.0064
B) 0.0301
C) 0.1511
D) 0.1877
Nationwide Insurance would like to perform a chi-square test to investigate whether a
difference exists in the proportion of male and female teenagers who text while they
drive. A random sample of 80 male teenagers found that 50 indicated they texted while
driving. A random sample of 120 female teenagers found that 65 indicated they texted
while driving. The degrees of freedom for the chi-square critical value is ________.
A) 1
B) 2
C) 3
D) 4
AutoTrader.com would like to test if a difference exists in the median age of three
different types of vehicles currently on the road–trucks, cars, and vans. The following
data represent the age of a random sample of trucks, cars, and vans.
The appropriate nonparametric procedure for this analysis is the _________________
test.
A) Wilcoxon rank-sum
B) sign
C) Wilcoxon signed-rank
D) Kruskal-Wallis
In Delaware, cars are inspected each year using state-operated inspection centers. The
Wilmington center has three drive-through lanes where cars are inspected in a sequence
of steps. The following data show the number of minutes that a random sample of
drivers spent waiting and having their cars inspected in the three lanes each day of the
week.
The state of Delaware would like to perform a randomized block ANOVA to test for a
difference in the average times the drivers spend in the three lanes using the weekday as
a blocking factor with α = 0.05. The sum of squares between for these observations is
________.
A) 181.2
B) 202.6
C) 225.0
D) 257.9
AutoTrader.com would like to test if a difference exists in the age of three different
types of vehicles currently on the road–trucks, cars, and vans. The following data
represent the age of a random sample of trucks, cars, and vans.
The sum of squares within for these observations is ________.
A) 20.3
B) 22.4
C) 30.0
D) 41.8
Use the information below to answer the following question(s).
Hats-R-Us would like to produce a new design of hats for the upcoming Major league
Baseball World Series. They need to decide to produce a large quantity or small
quantity of hats prior to the event starting. Eventual demand for this new design will be
strong or weak with a 50/50 chance of each level occurring. The following table shows
the payoff for each combination of production size and demand level, in thousands of
dollars.
Hats-R-Us also has the option of conducting a market survey at a cost of $10,000 to
acquire more accurate information about the likelihood of each demand level. If the
survey results are positive, there is an 83% probability that the eventual demand for the
new hat design will be strong. If the survey results are negative, there is a 23%
probability that the eventual demand for the new hat design will be strong.
Construct a decision tree to answer the following set of questions.
The expected monetary value, in thousands of dollars, for a large production quantity if
Hats-R-Us conducts a market survey and the survey results are positive is _________.
A) $361.2
B) $438.0
C) $495.5
D) $560.3
Which levels of measurement are considered quantitative data?
A) interval and ratio
B) nominal and interval
C) nominal and ratio
D) nominal and ordinal
Use the information below to answer the following question(s).
The following decision tree is partially completed for a company that is deciding to
build a large or small facility for a new product that will face demand that is strong or
weak. The company has an option to perform a market survey that will cost $4,000 that
will predict a strong or weak market. The payoffs for each combination of facility size
and demand are also shown.
If the company decides not to conduct the survey, the expected monetary value of
building a large facility is ________.
A) “$700
B) $3,600
C) $4,000
D) $4,600
John’s commute time to work during the week follows the normal probability
distribution with a mean time of 26.7 minutes and a standard deviation of 5.1 minutes.
The interval around the mean that contains 99.7% of the commute times is ________.
A) 21.6, 31.8
B) 16.5, 36.9
C) 11.4, 42.0
D) 6.3, 47.1
The sample covariance can be equal to any value __________
A) between “1.0 and +1.0.
B) greater than or equal to zero.
C) other than zero.
D) between and .
The following data show the monthly rental for a random sample of one-bedroom
apartments in York, Pennsylvania.
Construct a cumulative relative frequency distribution for this data and determine the
probability a randomly selected one-bedroom apartment will rent for less than $700 per
month.
A restaurant manager randomly selects tables at which customers have just been seated
and records the amount of time it takes for the wait staff to greet these customers. This
is an example of an experiment being used to collect data.
The following table shows the percentage of U.S. energy consumption according to
various sources.
Which of the following best displays this data?
A) horizontal bar chart
B) vertical bar chart
C) pie chart
D) histogram
According to Bureau of Labor Statistics, 26.0% of the total part-time workforce in the
U.S. was between the ages of 25 and 34 during a recent month. A random sample of 90
part-time employees was selected during this month. Using the normal approximation
to the binomial distribution, what is the probability that more than 27 people from this
sample were between the ages of 25 and 34?
A) 0.0668
B) 0.1025
C) 0.1611
D) 0.3034
A random sample of 30 business students required an average of 43.4 minutes to
complete a statistics exam. Assume that the population standard deviation to complete
the exam was 8.7 minutes. The margin of error for a 98% confidence interval around
this sample mean is ________.
A) 2.04
B) 2.62
C) 3.12
D) 3.70
YouTube would like to test the hypothesis that the average length of an online video
watched by a user is more than 8 minutes. A random sample of 37 people watched
online videos that averaged 8.7 minutes in length. It is believed that the population
standard deviation for the length of online videos is 2.5 minutes. YouTube would like to
set α = 0.02. The conclusion for this hypothesis test would be that because the test
statistic is _____________________.
A) more than the critical value, we can conclude that the average length of an online
video is more than 8 minutes
B) more than the critical value, we can conclude that the average length of an online
video is not more than 8 minutes
C) less than the critical value, we can conclude that the average length of an online
video is more than 8 minutes
D) less than the critical value, we can conclude that the average length of an online
video is not more than 8 minutes
Use the information below to answer the following question(s).
Steve Taylor is the owner of Home Plus, which is a chain of home improvement stores.
He would like to investigate the relationship between month advertising and monthly
sales. The table below shows the amount spent on advertising, in millions of dollars,
over several months along with the corresponding sales, also in millions of dollars.
Use the Home Plus data to:
A) Calculate the coefficient of determination.
B) Interpret the meaning of the coefficient of determination.
C) Test the significance of the coefficient of determination using α = 0.05.
John Charleston owns a heating oil delivery company that services 1,540 residences.
John would like to estimate the number of customers that have oil storage tanks that are
less than 100 gallons in capacity. A random sample of 200 customers found that 48 had
an oil tank that was less than 100 gallons. The 99% confidence interval to estimate the
proportion of customers with oil tanks less than 100 gallons is ________.
A) (0.212, 0.268)
B) (0.225, 0.255)
C) (0.167, 0.313)
D) (0.184, 0.296)
The table below shows the number of cars sold last month by seven employees at
Concord Motors and their number of years of sales experience.
Management would like to use simple regression analysis to estimate monthly car sales
using the number of years of sales experience. The y-intercept for the regression
equation is ________.
A) 2.165
B) 4.598
C) 6.940
D) 8.337
Use the following information to answer the question(s) below.
A home appraisal company would like to develop a regression model that would predict
the selling price of a house based on the age of the house in years (Age), the living area
of the house in square feet (Living Area) and the number of bedrooms (Bedrooms). The
following Excel output shows the partially completed regression output from a random
sample of homes that have recently sold.
Which one of the following statements describes the results of the hypothesis test for
the overall regression model using α = 0.05?
A) Because the test statistic is greater than the critical value, we reject the null
hypothesis and conclude that there is a relationship between the dependent variable and
the independent variables.
B) Because the test statistic is greater than the critical value, we fail to reject the null
hypothesis and conclude that there is a relationship between the dependent variable and
the independent variables.
C) Because the test statistic is less than the critical value, we fail to reject the null
hypothesis and conclude that there is no relationship between the dependent variable
and the independent variables.
D) Because the test statistic is less than the critical value, we reject the null hypothesis
and conclude that there is no relationship between the dependent variable and the
independent variables.
________ are the number of different ways in which objects can be arranged without
regard to order.
A) Simple events
B) Permutations
C) Random variables
D) Combinations
A ________ sample does not represent the intended population and can lead to distorted
findings.
A) random
B) probability
C) biased
D) stratified
In Delaware, cars are inspected each year using state-operated inspection centers. The
Wilmington center has three drive-through lanes where cars are inspected in a sequence
of steps. The following data show the number of minutes that a random sample of
drivers spent waiting and having their cars inspected in the three lanes each day of the
week.
The state of Delaware would like to perform a randomized block ANOVA to test for a
difference in the average times the drivers spend in the three lanes using the weekday as
a blocking factor with α = 0.05. The blocking factor test statistic for this hypothesis test
would be ________.
A) 5.08
B) 6.98
C) 8.17
D) 9.08
Spencer is the owner of Island Art, which sells artwork in a beach community in New
Jersey. The following data represent the number of 13×19 prints sold in the store from a
random sample of days.
Spencer would like to know if the daily demand for 13×19 prints follows the normal
probability distribution with μ = 10.0 and σ = 5.0 using α = 0.01. Perform this
hypothesis test.
State University offers several sections of a Business Statistics course in an in-class and
online format. Both formats are administered the same final exam each year. You have
been assigned to test the hypothesis that the standard deviation for the final exam score
of in-class students is different from the standard deviation of the final exam score of
online students. The following data summarizes the sample statistics for the final exam
scores for students from each format.
Test the hypothesis using α = 0.05.
Edmunds.com would like to test the hypothesis that the average age of an imported car
on the road is greater than the average age of a domestic car. The following data shows
the sample size and the average age of cars for import and domestic cars along with the
population standard deviations.
Define Population 1 as import cars and Population 2 as domestic cars and use the
critical value approach to test this hypothesis with α = 0.05.
Note: The problems below use the following information:
The following table show the standardized math exam scores for a random sample of
students for three states. The sample included an equal number of eight-graders and
fourth-graders.
A two-way ANOVA was performed using α = 0.05 by defining Factor A as the state and
Factor B as to whether the student was an eighth-grader or a fourth-grader. The results
are shown below.
Test the effects that the state and the grade of the student have on the standardized math
score.
AT&T would like to test the hypothesis that the standard deviation for the revenue per
retail user for Verizon Wireless customers is less than $11.00. The monthly revenue for
a random sample of 19 Verizon Wireless customers was recorded. The standard
deviation for this sample was found to be $9.60. Test this hypothesis using α = 0.01.
Suppose Citibank would like to investigate if credit score and age of an individual are
independent of one another. Citibank selected a random sample of 400 adults and asked
them to report their credit score range and their age range. The following contingency
table presents these results.
Perform a hypothesis test to determine if the credit score and the age of the individual
are independent variables using α = 0.05.
A business school has 15 full-time faculty and seven of them have tenure. A random
sample of six faculty are randomly selected to form a committee. What is the
probability that fewer than two of the faculty on the committee have tenure?
