The model y =
0+
1x1+
2x2+
3x3+
is a first-order regression model.
In a multiple regression model, the proportion of the variation of the dependent
variable, y, accounted for the independent variables in the regression model is given by
the coefficient of multiple correlation.
The number of degrees of freedom in a chi-square goodness-of-fit test is the number of
categories minus the number of parameters estimated minus one.
A researcher is interested in using a chi-square test of independence to determine if age
is independent of minutes spent reading. Age is divided into four categories while
minutes spent reading is classified as high, medium, low. The number of degrees of
freedom for this test is 12.
Control charts are used to examine the output of a process for disturbing patterns or for
data points that indicate that the process is out of control.
In statistics, the Winters’ Three Parameter statistic is a test statistic used to detect the
presence of autocorrelation in the residuals from a regression analysis.
In experimental design, a characteristic of the subjects that was present prior to the
experiment and is not the result of the experimenter’s manipulations or control is called
a classification variable.
If every unit of the population has the same probability of being selected to the sample,
then the researcher is probably conducting random sampling.
A graphical representation of a frequency distribution is called a pie chart.
The manner in which numerical data can be analyzed statistically depends on the level
of data measurement represented by numbers being analyzed.
Given two events A and B each with a non-zero probability, if the conditional
probability of A given B is zero, it implies that the events A and B are mutually
exclusive.
In a chi-square test of independence the contingency table has 4 rows and 3 columns.
The number of degrees of freedom for this test is 7.
Like a t-distribution, a chi-square distribution is symmetrical and extends from minus
infinity to plus infinity.
In a decision analysis problem, variables (such as benefits or rewards that result from
investments in common stocks or corporate bonds and from a new product launch)
which result from selecting a particular decision alternative are called posterior
probabilities.
In the one-sample runs test for randomness of the observations in a large sample (i.e.,
the number of observations with each of two possible characteristics is greater than 20)
the sampling distribution of R, the number of runs, is approximately binomial.
In testing a hypothesis about a population mean with an unknown population standard
deviation (
) the degrees of freedom is used in the denominator of the test statistic.
Normal distribution is a symmetrical distribution with its tails extending to infinity on
either side of the mean.
If a process is in control, less than 0.3% of all the points that represent the process
output such as the average measurement or the proportion defective should be beyond
the upper and lower control limits.
A scatter plot is useful for examining the relationship between two numerical variables.
The difference between the highest number and the lowest number in a set of data is
called the differential frequency.
The Poisson distribution is best suited to describe occurrences of rare events in a
situation where each occurrence is independent of the other occurrences.
Determining the table value for theF distribution requires two values for degrees of
freedom.
If the occurrence of one event does not affect the occurrence of another event, then the
two events are mutually exclusive.
The normal approximation for binomial distribution can be used when n=10 and p=1/5.
In experimental design, a variable that the experimenter controls or modifies in the
experiment is called a treatment variable.
The area under the standard normal distribution between -1 and 1 is twice the area
between 0 and 1.
One advantage of a stem and leaf plot over a frequency distribution is that the values of
the original data are retained.
If the median of a distribution is greater than mean, then the distribution is skewed to
the left.
A slope in a multiple regression model is known as a partial slope because it ignores the
effects of other explanatory variables.
The regression model y =
0+
1x1+
2x2+
3x1x2+
is a first order model.
The nonparametric alternative to analysis of variance for a randomized block design is
the Friedman test.
A descriptive measure of the sample is called a statistic.
A binomial distribution is better than a Poisson distribution to describe the occurrence
of major oil spills in the Gulf of Mexico.
For a binomial distribution in which the probability of success is p = 0.5, the variance is
twice the mean.
In a binomial experiment, any single trial contains only two possible outcomes and
successive trials are independent.
The value of sample information is the difference between the expected monetary value
with information to the expected monetary value without information.
One of the ways to overcome the autocorrelation problem in a regression forecasting
model is to transform the variables by taking the first-differences.
The concept of utility can be helpful to apply decision analysis techniques to situations
which do not lend themselves to expected monetary value analysis.
Inferring the value of a population parameter from the statistic on a random sample
drawn from the population is an inferential process under uncertainty.
Skewness and kurtosis of a data set are measures of the shape of the distribution.
Abel Alonzo, Director of Human Resources, is exploring employee absenteeism at the
Harrison Haulers Plant. Abel knows that absenteeism varies significantly between
departments. For example, workers in the wood shop are absent more than those in the
tuning department and the size of the departments ranges from 40 to 120 workers. He
orders a random sample of 10 workers from each of the six departments. Abel’s sample
is a ________________.
a) proportionate systematic sample
b) proportionate stratified sample
c) disproportionate systematic sample
d) disproportionate stratified sample
e) proportionate cluster sample
Data from a completely randomized design are shown in the following table.
For a one-way ANOVA, the Total Sum of Squares (SST) is ________.
a) 36.17
b) 28.75
c) 64.92
d) 18.03
e) 28.04
The following data is to be used to construct a regression model:
The regression equation is _______________.
a) y = 16.49 + 1.43x
b) y = 1.19 + 0.91x
c) y = 1.19 + 0.75x
d) y = 0.75 + 0.18x
e) y = 0.91 + 4.06x
An appropriate method to identify multicollinearity in a regression model is to ____.
a) examine a residual plot
b) examine the ANOVA table
c) examine a correlation matrix
d) examine the partial regression coefficients
e) examine the R2of the regression model
A useful technique in controlling multicollinearity involves the _________.
a) use of variance inflation factors
b) use the backward elimination procedure
c) use the forward elimination procedure
d) use the forward selection procedure
e) use all possible regressions
Consider the following scatter plot and regression line. At x = 50, the residual (error
term) is _______.
a) positive
b) zero
c) negative
d) imaginary
e) unknown
Sarah Soliz, Director of Quality Programs, is designing and R charts for the
rod shearing process at Stockton Steel. She has 26 samples of rod length, and each
sample included measurements of 5 rods. The mean of the 26 sample means is 112
inches, and mean of the 26 ranges is 0.15 inch. The upper control limit for her R chart is
____.
a) 0.150
b) 10.57
c) 0.317
d) 2.114
e) 0.713
Tamara Hill, fund manager of the Hill Value Fund, manages a portfolio of 250 common
stocks. Tamara is searching for a ‘low risk’ issue to add to the portfolio, i.e., one with a
price variance less than that of the S&P 500 index. Moreover, she assumes an issue is
not ‘low risk’ until demonstrated otherwise. Her staff reported that during the last nine
quarters the price variance for the S&P 500 index (population 1) was 25, and for the last
seven quarters the price variance for XYC common (population 2) was 8. Assume that
stock prices are normally distributed in the population. Using
= 0.05, Tamara’s null
hypothesis is _______.
a)
b)
c)
d)
e) s s
The expected (mean) life of a particular type of light bulb is 1,000 hours with a standard
deviation of 50 hours. The life of this bulb is normally distributed. What is the
probability that a randomly selected bulb would last fewer than 1100 hours?
a) 0.4772
b) 0.9772
c) 0.0228
d) 0.5228
e) 0.5513
The local oil changing business is very busy on Saturday mornings and is considering
expanding. A national study of similar businesses reported the mean number of
customers waiting to have their oil changed on Saturday morning is 3.6. Suppose the
local oil changing business owner, wants to perform a hypothesis test. The null
hypothesis is the population mean is 3.6 and the alternative hypothesis is the population
mean is not equal to 3.6. The owner takes a random sample of 16 Saturday mornings
during the past year and determines the sample mean is 4.2 and the sample standard
deviation is 1.4. It can be assumed that the population is normally distributed. The level
of significance is 0.05. The decision rule for this problem is to reject the null hypothesis
if the observed “t” value is _______.
a) less than -2.131 or greater than 2.131
b) less than -1.761 or greater than 1.761
c) less than -1.753 or greater than 1.753
d) less than -2.120 or greater than 2.120
e) less than -3.120 or greater than 3.120
Ray Crofford is evaluating investment alternatives for the $100,000 which he inherited
from his grandfather. His investment advisor has identified four alternatives and
constructed the following table which shows expected profits (in $10,000’s) for various
market conditions and their probabilities.
The expected value of perfect information is ________.
a) $57,000
b) $63,000
c) $79,000
d) $82,000
e) $87,000
The following ANOVA table is from a multiple regression analysis with n = 35 and four
independent variables.
The MSR value is __________.
a) 700.00
b) 350.00
c) 233.33
d) 175.00
e) 275.00
A time series with forecast values and error terms is presented in the following table.
The mean absolute deviation (MAD) for this forecast is ___________.
a) 3.54
b) 7.41
c) 4.43
d) 17.72
e) 4.34
Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in
the payroll system, and orders an inspection of “each and every payroll voucher issued
since January 1, 1993.” Each payroll voucher was inspected and the following
frequency distribution was compiled.
The mean number of errors per voucher is __________.
a) 3.67
b) 5
c) 750
d) 300
e) 8.7
If x, the time (in minutes) to complete an oil change job at certain auto service station,
is uniformly distributed over the interval 20 to 30, inclusively (20 x 30), then the height
of this distribution, f(x), is __________________.
a) 1/10
b) 1/20
c) 1/30
d) 12/50
e) 1/60
In a set of 12 aluminum castings, two castings are defective (D), and the remaining ten
are good (G). A quality control inspector randomly selects three of the twelve castings
with replacement, and classifies each as defective (D) or good (G). The sample space
for this experiment contains __________ elementary events.
a) 1,728
b) 220
c) 120
d) 10
e) 66
Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of
alternative toothpaste packages. She wonders whether acceptance is influenced by
children in the household. Her staff prepared the following contingency table from a
random sample of 100 households.
Using
= .05, the observed value of chi-square is ______________.
a) 5.28
b) 9.49
c) 13.19
d) 16.79
e) 18.79
The staff of Mr. Wayne Wertz, VP of Operations at Portland Peoples Bank, prepared a
cumulative frequency ogive of waiting time for walk-in customers.
The percentage of walk-in customers waiting more than 6 minutes was ______.
a) 22%
b) 11%
c) 67%
d) 10%
e) 75%
A multiple regression analysis produced the following tables.
The regression equation for this analysis is ____________.
a) y = 1959.71 + 0.46 x1 + 2.16 x2
b) y = 1959.71 – 0.46 x1 + 2.16 x2
c) y = 1959.71 – 0.46 x1 – 2.16 x2
d) y =1959.71 + 0.46 x1 – 2.16 x2
e) y =- 0.46 x1 ” 2.16 x2
Consider the following null and alternative hypotheses.
Ho:
= 67
Ha:
67
These hypotheses ______________.
a) indicate a one-tailed test with a rejection area in the right tail
b) indicate a one-tailed test with a rejection area in the left tail
c) indicate a two-tailed test
d) are established incorrectly
e) are not mutually exclusive
Given P(A) = 0.40, P(B) = 0.50, P(A B) = 0.15. Find P(A B).
a) 0.90
b) 1.05
c) 0.75
d) 0.65
e) 0.60
In an instant lottery, your chance of winning is 0.1. If you play the lottery 100 times and
outcomes are independent, the probability that you win at least 15 percent of the time is
a) 0.4933
b) 0.5
c) .15
d) 0.0478
e) 0.9213
Jack Joyner, Director of Quality Control at Covington Castings (CC), is designing a c
chart to monitor the number of nonconformances per aluminum casting produced at
CC. The total number of nonconformances for 26 castings is 91. The upper control limit
for Jack’s c chart is ___________.
a) 9.11
b) 13.40
c) 3.50
d) 7.61
e) 1.00
Ophelia O’Brien, VP of Consumer Credit of American First Banks (AFB), monitors the
default rate on personal loans at the AFB member banks. One of her standards is “no
more than 5% of personal loans should be in default.” On each Friday, the default rate
is calculated for a sample of 500 personal loans. Last Friday’s sample contained 30
defaulted loans. Using
= 0.01, critical chi-square value is _______.
a) 6.63
b) 9.21
c) 7.88
d) 10.60
e) 12.34
The Wilcoxon test was used on 16 pairs of data. The total of the ranks (T) were
computed to be 76 (for + ranks) and 60 (for – ranks). The zvalue for this test is _____.
a) -0.41
b) -0.02
c) 0.02
d) 16
e) -0.041.
At a certain workstation in an assembly line, the time required to assemble a component
is exponentially distributed with a mean time of 10 minutes. Find the probability that a
component is assembled in 7 minutes or less?
a) 0.349
b) 0.591
c) 0.286
d) 0.714
e) 0.503
Velma Vasquez, fund manager of the Vasquez Value Fund, manages a portfolio of 250
common stocks. Velma relies on various statistics, such as variance, to assess the
overall risk of stocks in an economic sector. Her staff reported that for a sample 14
utility stocks the mean annualized return was 14% and that the variance was 3%.
Assume that annualized returns are normally distributed. The 90% confidence interval
for the population variance of annualized returns is _______.
a) 0.018 to 0.064
b) 0.016 to 0.078
c) 0.017 to 0.066
d) 0.016 to 0.075
e) 0.020 to 0.080
Let zbe a normal random variable with mean 0 and standard deviation 1. What is P(1.3
< z< 2.3)?
a) 0.4032
b) 0.9032
c) 0.4893
d) 0.0861
e) 0.0086
A cost accountant is developing a regression model to predict the total cost of
producing a batch of printed circuit boards as a linear function of batch size (the
number of boards produced in one lot or batch), production plant (Kingsland, and
Yorktown), and production shift (day, and evening). The response variable in this model
is ______.
a) batch size
b) production shift
c) production plant
d) total cost
e) variable cost
Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment
and supplies, is reviewing the order filling operations at her warehouses. Her goal is
100% of orders shipped within 24 hours. In previous years, neither warehouse has
achieved the goal, but the East Coast Warehouse has consistently out-performed the
West Coast Warehouse. Her staff randomly selected 200 orders from the West Coast
Warehouse (population 1) and 400 orders from the East Coast Warehouse (population
2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the
East Coast Warehouse shipped 372 orders within 24 hours. Assuming
= 0.05, the
critical zvalue is ___________________.
a) -1.96
b) -1.64
c) 1.64
d) 1.96
e) 2.33
Catherine Chao, Director of Marketing Research, needs a sample of Kansas City
households to participate in the testing of a new toothpaste package. If 40% of the
households in Kansas City prefer the new package, the probability that Catherine’s
random sample of 300 households will have a sample proportion between 0.35 and 0.45
is ___________.
a) 0.9232
b) 0.0768
c) 0.4616
d) 0.0384
e) 0.8976
Abel Alonzo, Director of Human Resources, is exploring employee absenteeism at the
Harrison Haulers Plant. Abel knows that absenteeism varies significantly between
departments. For example, workers in the wood shop are absent more than those in the
tuning department and the size of the departments ranges from 40 to 120 workers. He
orders a random sample of 10% of the workers from each of the six departments. Abel’s
sample is a ________________.
a) proportionate systematic sample
b) proportionate stratified sample
c) disproportionate systematic sample
d) disproportionate stratified sample
e) proportionate cluster sample
A manager wishes to predict the annual cost (y) of an automobile based on the number
of miles (x) driven. The following model was developed: y = 2,000 + 0.42x. If a car is
driven 20,000 miles, the predicted cost is ____________.
a) 10,400
b) 20,000
c) 2,840
d) 6,200
e) 6,750