In a multiple regression model, R-square can be computed by squaring the highest
correlation coefficient between the dependent variable and any independent variable.
The distribution for the number of emergency calls to a city’s 911 emergency number in
a one-hour time period is likely to be described by a binomial distribution.
The following probability distribution was subjectively assessed for the number of sales
a salesperson would make if he or she made five sales calls in one day.
Given this distribution, the probability that the number of sales is more than 2 is 0.80.
The Kruskal-Wallis test is used to test whether the centers of 3 or more populations are
equal so long as that is the only possible difference between the population
distributions.
If a six-sided die is tossed two times and “4” shows up both times, the probability of “4”
on the third trial is much larger than any other outcome.
One of the major automobile makers has developed two new engines. At question is
whether the two engines have the same variability with respect to miles per gallon. To
test this, the following information is available:
Based on this situation and the information provided, the appropriate null and
alternative hypotheses are:
H0 : ≠
Ha : =
The difference between interval data and ratio data is that interval data has a natural
zero.
A sampling distribution is the distribution of the individual values that are included in a
sample from a population.
The director of the city Park and Recreation Department claims that the mean distance
people travel to the city’s greenbelt is more than 5.0 miles. Assuming that the
population standard deviation is known to be 1.2 miles and the significance level to be
used to test the hypothesis is 0.05 when a sample size of n = 64 people are surveyed, the
probability of a Type II error is approximately .4545 when the “true” population mean is
5.5 miles.
A two-tailed hypothesis test is used when the null hypothesis looks like the following:
H0: = 100.
The frequency distribution of most processes’ statistics will begin to resemble the shape
of the normal distribution as the values are collected and grouped into classes.
A one-tailed hypothesis test for a population variance always has the rejection region in
the upper tail.
Models can be specified as linear or nonlinear.
Given a sample of data for use in simple linear regression, the values for the slope and
the intercept are chosen to minimize the sum of squared errors.
A smaller sample might provide less sampling error than a larger sample from a given
population.
From an annual time series of a company’s sales the linear trend model Ft = 127 + 54(t)
has been developed. This means that on average sales have been increasing by 127 per
year.
The standard normal distribution has a mean of 0 and a standard deviation of 1.0.
A two-tailed test for two population variances could have a null hypothesis like the
following:
H0 : =
In preparing a line chart, the horizontal axis shows time and the vertical axis shows the
value of the variable of interest.
The Varden Packaging Company has a contract to fill 50 gallon barrels with gasoline
for use by the U.S. Army. The machine that Varden uses has an adjustable device that
allows the average fill per barrel to be adjusted as desired. However, the actual
distribution of fill volume from the machine is known to be normally distributed with a
standard deviation equal to 0.5 gallons. The contract that Varden has with the military
calls for no more than 2 percent of all barrels to contain less than 49.2 gallons of
gasoline. In order to meet this requirement, Varden should set the mean fill to
approximately 49.92 gallons.
Two confidence interval estimates were developed from the same sample of a
population. The wider interval will be the one that has the higher confidence level.
If the sample data lead us to suspect that the variances of the two populations are not
equal, the t-test statistic and the degrees of freedom must be adjusted accordingly.
When people fail to respond to a survey, the data collection process may suffer from
nonresponse bias.
A scatter diagram can show whether a pair of variables has a strong or weak
relationship, and also whether it is linear or curved.
The frequency distribution of most processes’ statistics will begin to resemble the shape
of the normal distribution as the values are collected and grouped into classes.
There is interest at the American Savings and Loan as to whether there is a difference
between average daily balances in checking accounts that are joint accounts (two or
more members per account) versus single accounts (one member per account). To test
this, a random sample of checking accounts was selected with the following results:
Based upon these data, assuming that the populations are normally distributed with
equal variances, the test statistic for testing whether the two populations have equal
means is approximately -1.49.
A study was recently done in which the following regression output was generated
using Excel.
SUMMARY OUTPUT
Given this, we know that approximately 57 percent of the variation in the y variable is
explained by the x variable.
In a hypothesis test involving two population variances, if the null hypothesis states that
the two variances are strictly equal, then the test statistic is a chi-square statistic.
The State Department of Forests has determined that annual tree growth in a particular
forest area is normally distributed with a mean equal to 17 inches and a standard
deviation equal to 6 inches. Based on this information, it is possible for a randomly
selected tree not to have grown any during a year.
A cell phone company believes that 90 percent of its customers are satisfied with their
service. They survey n = 30 customers. Based on this, it is acceptable to assume the
sample distribution is normally distributed.
In most situations, there is no difference between the events and the elementary events.
A goodness-of-fit test can decide whether a set of data comes from a specific
hypothesized distribution.
In a recent report to the supply-chain manager in a major electronics company, the
report writer stated that with 90 percent confidence, the manufacturing lead time for a
critical part is between 3.34 hours and 4.14 hours. Based on this information, the
margin of error for this estimate is .80 hours.
The Cromwell Construction Company has the opportunity to enter into a contract to
build a mountain road. The following table shows the probability distribution for the
profit that could occur if it takes the contract:
Based on this information, the expected profit for the company if it takes the contract is
$70,500.
The NCAA is interested in estimating the difference in mean number of daily training
hours for men and women athletes on college campuses. It wants 95 percent confidence
and will select a sample of 10 men and 10 women for the study. The variances are
assumed equal and the populations normally distributed. The sample results are:
Based on these sample data, the critical value for developing the confidence interval is z
= 1.96.
To find a 98 percent confidence interval where the standard deviation is known, the
correct z-value to use for the critical value is 2.33.
The amount of drying time for the paint applied to a plastic component part is thought
to be uniformly distributed between 30 and 60 minutes. Currently, the automated
process selects the part from the drying bin after the part has been there for 50 minutes.
The probability that none of three parts picked are still wet when they are selected is
approximately 0.04.
Sampling error is the difference between a statistic computed from a sample and the
corresponding parameter computed from the population.
A survey was recently conducted in which males and females were asked whether they
owned a laptop personal computer. The following data were observed:
Given this information, if an alpha level of .05 is used, the sum of the expected cell
frequencies will be equal to the sum of the observed cell frequencies.
A contract calls for the mean diameter of a cylinder to be 1.50 inches. As a quality
check, each day a random sample of n = 36 cylinders is selected and the diameters are
measured. Assuming that the population standard deviation is thought to be 0.10 inch
and that the test will be conducted using an alpha equal to 0.025, what would the
probability of a Type II error be?
A) Approximately 0.1267
B) About 0.6789
C) 0.975
D) Can’t be determined without knowing the “true” population mean.
The degrees of freedom for the chi-square goodness-of-fit test are equal to ________,
where k is the number of categories.
A) k + 1
B) k – 1
C) k + 2
D) k – 2
Based on weather data collected in Racine, Wisconsin, on Christmas Day, the weather
had the following distribution:
/Thompson_sn3t_WordExports/Thompson_sn3t_WordExports
Based on these data, what is the probability that next Christmas will be dry?
A) 0.45
B) 0.50
C) 0.60
D) 0.70
Which of the following questions CANNOT be answered using a scatter diagram?
A) What is the trend over time of each of the 2 variables?
B) Is there a curved or linear relation between the 2 variables?
C) Is there a weak or strong relation between the 2 variables?
D) Is there a positive or negative relation between the 2 variables?
A random variable, x, has a normal distribution with μ = 13.6 and σ = 2.90. Determine a
value, x0, so that P(x ≤ x0) = 0.975.
A) 16.678
B) 19.284
C) 23.360
D) 14.475
Each year, Business Week publishes information and rankings of master of business
administration (MBA) programs. The data file MBA Analysis contains data on several
variables for eight reputable MBA programs as presented in the October 2, 2000, issue
of Business Week. The variables include pre- and post-MBA salary, percentage salary
increase, undergraduate GPA, average Graduate Management Admission Test (GMAT)
score, annual tuition, and expected annual student cost. Compute the mean and median
for each of the variables in the database.
A)
B)
C)
D)
The asking price for homes on the real estate market in Baltimore has a mean value of
$286,455 and a standard deviation of $11,200. Four homes are listed by one real estate
company with the following prices:
Based upon this information, which house has a standardized value that is relatively
closest to zero?
A) Home 1
B) Home 2
C) Home 3
D) Home 2 and home 3
A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays
(Monday through Friday). It has collected the following data based on a random sample
of 100 days.
What is the value of the test statistic needed to conduct a goodness-of-fit test?
A) 8.75
B) 7.7794
C) 2.46
D) 2.50
A histogram can be created for discrete or continuous data.
You are given the following results of a paired-difference test:
= -4.6
sd = 0.25
n = 16
Construct a 90% confidence interval estimate for the paired difference in mean values.
A) -2.86 ——- -2.53
B) -5.72 ——- -5.18
C) -3.81 ——- -3.71
D) -4.71 ——- -4.49
You are given the following null and alternative hypotheses:
If the true population mean is 4,345, determine the value of beta. Assume the
population standard deviation is known to be 200 and the sample size is 100.
A) 0.9192
B) 0.8233
C) 0.6124
D) 0.0314
Suppose it is known that the income distribution in a particular region is right-skewed
and bi-modal. If bank economists are interested in estimating the mean income, which
of the following is true?
A) Provided that the sample size is sufficiently large, the sampling distribution for
will be approximately normal with a mean equal to the population mean that they wish
to estimate.
B) The sampling distribution will also be right-skewed for large sample sizes.
C) The standard deviation of the sampling distribution for will be proportionally
larger than the population standard deviation, depending on the size of the sample.
D) The sampling distribution will be left-skewed.
What method of probability assessment would most likely be used to assess the
probability that a major earthquake will occur in California in the next three years?
A) Classical probability based on the ratio of the number of ways the event can occur
B) Relative frequency based on previous history
C) Subjective probability based on expert opinion
D) Independent probability based on two unrelated outcomes
The manager at a local movie theater has collected data for a long period of time and
has concluded that the revenue from concession sales during the first show each
evening is normally distributed with a mean equal to $336.25 and a variance equal to
1,456. Based on this information, what are the chances that the revenue on the first
show will exceed $800?
A) 0.1255
B) Essentially zero
C) 0.3745
D) 0.9999
The General Electric service department believes that the median time for a service call
should be 30 or fewer minutes. To test this, the following random sample of service
times was collected:
Given that the managers do not wish to make the assumption that the population is
normally distributed, the test statistic for the Wilcoxon signed rank sum test is:
A) W = 43.0
B) W = 27.0
C) W = 18.0
D) None of the above
In a multiple regression model, which of the following is true?
A) The coefficient of determination will be equal to the square of the highest correlation
in the correlation matrix.
B) Adding variables that have a low correlation with the dependent variable will cause
the R-square value to decline.
C) The sum of the residuals computed for the least squares regression equation will be
zero.
D) The adjusted R-square might be higher or lower than the value of the R-square.
A scatter diagram can be used to do which of the following?
A) Determine the trend in a variable
B) Analyze the relationship between two variables
C) Describe the basic distribution for a quantitative variable
D) Show the percentage of a variable that is associated with each category into which
that variable has been divided
Which of the following will increase the width of a confidence interval (assuming that
everything else remains constant)?
A) Decreasing the confidence level
B) Increasing the sample size
C) A decrease in the standard deviation
D) Decreasing the sample size
The State Transportation Department is thinking of changing its speed limit signs. It is
considering two new options in addition to the existing sign design. At question is
whether the three sign designs will produce the same mean speed. To test this, the
department has conducted a limited test in which a stretch of roadway was selected.
With the original signs up, a random sample of 30 cars was selected and the speeds
were measured. Then, on different days, the two new designs were installed, 30 cars
each day were sampled, and their speeds were recorded. Suppose that the following
summary statistics were computed based on the data:
The appropriate test to conduct to determine if the population means are equal is:
A) Hartley’s F-max test.
B) one-way analysis of variance.
C) three sample t-test.
D) randomized complete block analysis of variance.
Statistics are measures computed from the entire population of data.
The U.S. Golf Association provides a number of services for its members. One of these
is the evaluation of golf equipment to make sure that the equipment satisfies the rules of
golf. For example, they regularly test the golf balls made by the various companies that
sell balls in the United States. Recently, they undertook a study of two brands of golf
balls with the objective to see whether there is a difference in the mean distance that the
two golf ball brands will fly off the tee. To conduct the test, the U.S.G.A. uses a robot
named “Iron Byron,” which swings the club at the same speed and with the same swing
pattern each time it is used. The following data reflect sample data for a random sample
of balls of each brand.
Given this information, what is the test statistic for testing whether the two population
variances are equal?
A) Approximately F = 1.145
B) t = 1.96
C) t = -4.04
D) None of the above
The Hilbert Drug Store owner plans to survey a random sample of his customers with
the objective of estimating the mean dollars spent on pharmaceutical products during
the past three months. He has assumed that the population standard deviation is known
to be $15.50. Given this information, what would be the required sample size to
estimate the population mean with 95 percent confidence and a margin of error of
$2.00?
A) 231
B) 163
C) 16
D) 15
What method of probability assessment would most likely be used to assess the
probability that a customer will return a purchase for a refund?
A) Classical probability based on the ratio of the number of ways the event can occur
B) Relative frequency based on previous history
C) Subjective probability based on expert opinion
D) Independent probability based on two unrelated outcomes
The Canyon Water Company collects data on the number of gallons of water consumed
during a month for each customer. The production manager has divided the usage into 6
classes. To display these data effectively, she could use which of the following types of
graphs to convey information about the water usage?
A) A stem and leaf diagram
B) A bar chart
C) A histogram
D) Either a histogram or a pie chart
Which of the following statements is true in the context of a chi-square goodness-of-fit
test?
A) The degrees of freedom for determining the critical value will be the number of
categories minus 1.
B) The critical value will come from the standard normal table if the sample size
exceeds 30.
C) The null hypothesis will be rejected for a small value of the test statistic.
D) A very large test statistic will result in the null not being rejected.
If the population correlation between two variables is determined to be -0.70, which of
the following is known to be true?
A) There is a positive linear relationship between the two variables.
B) There is a fairly strong negative linear relationship between the two variables.
C) An increase in one of the variables will cause the other variable to decline by 70
percent.
D) The scatter diagram for the two variables will be upward sloping from left to right.
A manager is interested in testing whether three populations of interest have equal
population means. Simple random samples of size 10 were selected from each
population. The following ANOVA table and related statistics were computed:
Conduct the appropriate test of the null hypothesis assuming that the populations have
equal variances and the populations are normally distributed. Use a 0.05 level of
significance.
A) Using the F test approach, because F = 3.354 < critical F = 9.84, we reject the null
hypothesis and conclude that the population means are not all equal.
B) Using the F test approach, because F = 3.354 < critical F = 9.84, we do not reject the
null hypothesis and conclude that the population means are all equal.
C) Using the F test approach, because F = 9.84 > critical F = 3.35, we reject the null
hypothesis and conclude that the population means are not all equal.
D) Using the F test approach, because F = 9.84 > critical F = 3.35, we do not reject the
null hypothesis and conclude that the population means are all equal.
A study has recently been conducted by a major computer magazine publisher in which
the objective was to develop a multiple regression model to explain the variation in
price of personal computers. Three quantitative independent variables were used along
with one qualitative variable. The qualitative variable was coded 1 if the computer
included a monitor, 0 otherwise. The following computer printout shows the final
output.
Based on this information, and with a 0.05 level of significance, which of the following
conclusions can be justified?
A) Knowing whether the computer comes with a monitor or not is a significant factor in
explaining the variation in price of the computer.
B) There are substantial multicollinearity effects in this regression model.
C) The only significant variable in the model at the .05 level of significance is Hard
Drive Capacity.
D) Removing the Monitor dummy variable would reduce the standard error of the
estimate considerably.
Hillman Management Services manages apartment complexes in Tulsa, Oklahoma.
They currently have 30 units available for rent. The monthly rental prices (in dollars)
for this population of 30 units are:
What is the range of possible sampling error if a random sample of sizen = 10 is
selected?
A) -174.21 to 191.12
B) -182.59 to 169.91
C) -164.33 to 178.67
D) -162.16 to 171.51
The managers of a local golf course have recently conducted a study of the types of golf
balls used by golfers based on handicap. A joint frequency table for the 100 golfers
covered in the survey is shown below:
Based on these data, the probability of someone using a Strata ball and having a
handicap under 2 is:
A) 0.05
B) 0.38
C) 0.25
D) None of the above
Which of the following is true with respect to the binomial distribution?
A) As the sample size increases, the expected value of the random variable decreases.
B) The binomial distribution becomes more skewed as the sample size is increased for a
given probability of success.
C) The binomial distribution tends to be more symmetric as p approaches 0.5.
D) In order for the binomial distribution to be skewed, the sample size must be quite
large.
For the normal distribution with parameters μ = 5, σ= 2; calculate P(0 < x < 8).
A) 0.8023
B) 0.4152
C) 0.9270
D) 0.8845
Drake Marketing and Promotions has randomly surveyed 200 men who watch
professional sports. The men were separated according to their educational level
(college degree or not) and whether they preferred the NBA or the National Football
League (NFL). The results of the survey are shown:
What is the probability that a randomly selected survey participant prefers the NFL?
A) 0.5250
B) 0.2000
C) 0.6050
D) 0.5880
The Wilson Company is interested in forecasting demand for its XG-667 product for
quarter 13 based on 12 quarters of data. The following shows the data and the double
exponential smoothing model results for periods 1-12 using alpha = 0.20 and beta =
0.40
Based on this information, what is the difference between the forecast for period 13
using smoothing constants of alpha = 0.20 and beta = 0.40 and smoothing constants of
alpha = 0.10 and beta = 0.30? (Assume that the starting values for period 0 are C = 745
and T = 32.)
A) About 108 units
B) Approximately 9 units
C) Just under 32 units
D) About 85 units
If a continuous random variable is said to be exponentially distributed, what would be
the easiest way to reduce the standard deviation?
Explain what is meant by a p-value.
In creating a frequency distribution for numerical data, describe the steps in choosing
the classes.
What is meant by the terms Type I and Type II statistical error?
At the West-Side Drive-Inn, customers arrive at the rate of 10 every 30 minutes. The
time between arrivals is exponentially distributed. Based on this information, what is
the probability that the time between two customers arriving will exceed 6 minutes?
In discussing a confidence interval estimate for a population mean, is it acceptable to
provide an interpretation like the following: “There is a 95 percent chance that μ lies in
the range 20 to 40″?
Under what conditions should a decision maker use a nonparametric statistical
procedure?
If a manager is interested in estimating the mean time customers spend shopping in a
store on each visit to the store, she may want to develop a confidence interval estimate.
Suppose, she has determined the required sample size and feels that she cannot afford
one that large. What options are available?
What is meant by the term statistical inference?
A real estate agent believes that home with swimming pools take longer to sell than
home without swimming pools. A random sample of each type of recently sold homes
was taken where the number of days on the market is recorded. Results are:
Homes with pool Homes w/o
pool
Sample mean 77 days 65 days
Sample Standard deviation 8.4 days 7.2 days
Sample size 19 23
Assuming that the populations are normally distributed and the variances are equal,
conduct the appropriate hypothesis test to determine if the real estate agent is correct.
Use the 0.05 level of significance.
Explain the difference between a stratified random sample and cluster random sample.
Explain the basic logic behind the chi-square goodness-of-fit test.
Assume you are conducting a two-way ANOVA and have found a significant interaction
between the two factors. Explain what conclusions you can make from the results and
what if any further steps should be taken.
In comparing a uniform distribution with a normal distribution where both distributions
have the same mean and the same range, explain which distribution will have the larger
standard deviation.
What are the advantages and disadvantages of open-end questions in either a written
survey or a personal interview?
The annual income for independent sales representatives in the United States is thought
to be highly right-skewed with a mean equal to $144,300 and a standard deviation of
$32,450. Given this information, if a sample of 36 independent sales representatives is
selected, what is the probability that the mean of the sample will exceed $130,000?
In a recent audit report, an accounting firm stated that the mean sale per customer for
the client was estimated to be between $14.50 and $28.50. Further, this was based on a
random sample of 100 customers and was computed using 95 percent confidence.
Provide a correct interpretation of this confidence interval estimate.
The proportion of parts in an inventory that are outdated and no longer useful is thought
to be 0.10. To check this, a random sample of n = 100 parts is selected and 14 are found
to be outdated. Based upon this information, what is the probability of 14 or more
outdated parts?
