The mean of the binomial distribution is equal to
A. p.
B. np.
C. px(1 − p)n−x.
D. (n)(p)(1 − p).
E.
After plotting the data points on a scatter diagram, we have observed an inverse
relationship between the independent variable (X) and the dependent variable (Y).
Therefore, we can expect both the sample ___________ and the sample
_____________ to be negative values.
A. intercept, slope
B. slope, coefficient of determination
C. intercept, correlation coefficient
D. slope, correlation coefficient
E. slope, standard error of estimate
Suppose that 60 percent of a company’s computer chips are manufactured in Factory A,
while 40 percent are produced in Factory B [P(A) = .60 for a randomly selected chip].
The defect rates for the two factories are 35 percent for Factory A and 25 percent for
Factory B. Suppose we now know that the randomly selected chip is defective. Find the
probability that the defective chip comes from Factory A.
Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and
a standard deviation of 0.2 ounces. The weights of the sugar packages are normally
distributed. What is the probability that 16 randomly selected packages will have a
weight in excess of 16.075 ounces?
A. .0500
B. .3520
C. .9332
D. .0668
The chief chemist for a major oil and gasoline production company claims that the
regular unleaded gasoline produced by the company contains on average 4 ounces of a
certain ingredient. The chemist further states that the distribution of this ingredient per
gallon of regular unleaded gasoline is normal and has a standard deviation of 1.2
ounces. What is the probability of finding an average in excess of 4.3 ounces of this
ingredient from 100 randomly inspected 1-gallon samples of regular unleaded gasoline?
A. .5987
B. .4013
C. .9938
D. .0062
The purpose behind moving averages and centered moving averages is to eliminate
__________________.
A. constant variation
B. cyclical variation
C. seasonal variation
D. regular variation
Measurements from a population are called
A. elements.
B. observations.
C. variables.
D. processes.
Historical data for a local manufacturing company show that the average number of
defects per product produced is 2. In addition, the number of defects per unit is
distributed according to a Poisson distribution. What is the probability that there will be
a total of 7 defects on four units?
A. .8750
B. .1221
C. .0573
D. .1396
When we are choosing a random sample and we do not place chosen units back into the
population, we are
A. sampling with replacement.
B. sampling without replacement.
C. using a systematic sample.
D. using a voluntary response sample.
__________________ statistics is an area of statistics that uses a theorem to update
prior belief about a probability or population parameter to a posterior belief.
A. Bayesian
B. Utility theory
C. Preposterior analysis
D. Risk theory
If A and B are independent events, P(A) = .2, and P(B) = .7, determine
A. 0.90
B. 0.14
C. 0.76
D. 0.50
E. 0.24
When deseasonalizing a time series observation, we divide the actual time series
observation by its ___________.
A. irregular factor
B. cyclical factor
C. seasonal factor
D. weighted aggregate factor
Four employees who work as drive-through attendants at a local fast-food restaurant are
being evaluated. As part of a quality improvement initiative and employee evaluation,
these workers were observed over three days. One of the statistics collected was the
proportion of time the employee forgot to include a napkin in the bag. Related
information is given in the table.
You just purchased a dinner and found that there is no napkin in your bag. What is the
probability that Jan prepared your order?
A. 0.200
B. 0.004
C. 0.018
D. 0.076
E. 0.100
Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which
are defective. If one item is drawn from each container, what is the probability that both
items are not defective?
A. 0.3750
B. 0.3846
C. 0.1500
D. 0.6154
E. 0.2000
A professional organization is attempting to determine whether salaries of hospital
CFOs differ by geographical region. Five hospital CFOs were randomly selected from
each of the following four regions of the United States: East, Midwest, South, and West.
Each CFO was then asked his or her annual salary. The salary distributions were highly
skewed. The table below summarizes the results of the Kruskal-Wallis test obtained
from MegaStat/Excel.
At a significance level of .05, the rejection point condition for the hypothesis test is
A. reject H0 if χ2 > 9.3484.
B. reject H0 if χ2 > 30.1435.
C. reject H0 if χ2 > 7.81473.
D. reject H0 if χ2 > .341846.
E. reject H0 if χ2 > 32.8523.
If x is a Poisson random variable with a mean of 10, what is the probability that x is
greater than 6?
A. .9329
B. .7797
C. .8698
D. .0002
A simple index is computed by using the values of one time series, while a(n)
___________ index is based on a “market basket” consisting of more than one time
series.
A. weighted
B. aggregate
C. cyclical
D. trend
In a multiple regression analysis, if the normal probability plot ____________, then it
can be concluded that the assumption of normality is not violated.
A. is a straight line
B. has the shape of a symmetric bell-shaped curve
C. is greatly curved
D. is left skewed
E. has the shape of a parabola that opens upward
A random sample of size 36 is taken from a population with a mean of 50 and a
standard deviation of 5. The sampling distribution of ____________________.
A. cannot be determined
B. is skewed to the left
C. is approximately normal
D. is skewed to the right
If we consider the toss of four coins as an experiment, how many outcomes does the
sample space consist of?
A. 8
B. 4
C. 16
D. 32
E. 2
If p = .1 and n = 5, then the corresponding binomial distribution is ____________.
A. right skewed
B. left skewed
C. symmetric
D. bimodal
Employees of a local university have been classified according to gender and job type.
If an employee is selected at random, what is the probability that the employee is male
and salaried staff?
A. .15
B. .10
C. .38
D. .50
E. .85
As the difference between observed frequency and expected frequency
_______________, the probability of rejecting the null hypothesis increases.
A. stays the same
B. decreases
C. increases
D. goes to 0
Another name for the 50th percentile is the ___________.
A. mean
B. first quartile
C. median
D. mode
E. third quartile
A study conducted by a local university found that 25 percent of college freshmen
support increased spending on environmental issues. If 6 college freshmen are
randomly selected, find the probability that fewer than 4 support increased spending on
environmental issues.
A. .0330
B. .7844
C. .9624
D. .9954
A ______________ shows the relationship between two variables.
A. stem-and-leaf
B. bar chart
C. histogram
D. scatter plot
E. pie chart
The percentage of measurements in a class is called the ___________ of that class.
A. frequency
B. relative frequency
C. leaf
D. cumulative percentage
Find the coefficient of variation for IQ tests with a mean of 100 and a standard
deviation of 15.
A. 15.0
B. 6.7
C. 0.15
D. 1.5
E. 67
The constant return used to forecast future wealth based on actual time periods and their
returns is the ____________.
A. grouped mean
B. geometric mean
C. weighted mean
D. arithmetic mean
If a population distribution is skewed to the right, then, given a random sample from
that population, one would expect that the ____________.
A. median would be greater than the mean
B. mode would be equal to the mean
C. median would be less than the mean
D. median would be equal to the mean
The weight of a product is measured in pounds. A sample of 50 units is taken from a
recent production. The sample yielded = 75 lb, and we know that σ2 = 100 lb.
Calculate a 99 percent confidence interval for μ.
A. [71.36, 78.64]
B. [74.25, 75.75]
C. [38.58, 111.42]
D. [71.71, 78.29]
In a ___________________ experimental design, independent random samples of
experimental units are assigned to the treatments.
A. one-way ANOVA
B. two-way ANOVA
C. randomized block
D. balanced complete factorial
The ______________ of a sample statistic is the probability distribution of the
population of all possible values of the sample statistic.
A. sample mean
B. sampling Distribution of Sample Mean
C. probability
D. observations
Every current applicant for a position in the marketing department of Company A is
given a 10-question test on interpretation of findings from statistical analyses.
Individuals are rated on three levels based on their scores: Excellent (9-10 correct),
Average (5-8 correct), and Poor (fewer than 5 correct). Historically, the probability of
an individual scoring Excellent = .38, Average = .52, and Poor = .10. Also, the company
knows that 90 percent of applicants who score Excellent are offered a position, 75
percent of applicants who score Average are offered a position, and 35 percent of the
applicants who score Poor are offered a position. What is the probability that an
individual who is offered a position has an Average score?
Consider the following partial computer output from a simple linear regression analysis.
Test H0: β1 ≤ 0 vs. Ha: β1 > 0.
The binomial random variable x consists of n = 60 trials and has the probability of
failure q = 0.4. Using the normal approximation, compute the probability of 19
successes.
Fill in the missing components of the following frequency distribution constructed for a
sample size of 50.
Consider the following partial analysis of variance table from a randomized block
design with 10 blocks and 6 treatments.
Source SS
Treatments 2,477.53
Blocks 3,180.48
Error 11,661.38
Total
What is the calculated F statistic for blocks?
The 95 percent confidence interval for the average weight of a product is from 72.23 lb
to 77.77 lb. Can we conclude that μ = 77, using a 95 percent confidence interval?
A. Yes
B. No
A fast-food company uses two management-training methods. Method 1 is a traditional
method of training, and Method 2 is a new and innovative method. The company has
just hired 31 new management trainees. 15 of the trainees are randomly selected and
assigned to Method 1, and the remaining 16 trainees are assigned to Method 2. After
three months of training, the management trainees take a standardized test. The test is
designed to evaluate their performance and learning from the training. The sample
mean score and sample standard deviation of the two methods are given below.
Company management wants to determine whether the company should implement the
new training method.
Write the null and alternative hypotheses.
A local tire dealer wants to predict the number of tires sold each month. He believes
that the number of tires sold is a linear function of the amount of money invested in
advertising. He randomly selects 6 months of data consisting of tire sales (in thousands
of tires) and advertising expenditures (in thousands of dollars). Based on the data set
with 6 observations, the simple linear regression model yielded the following results.
Determine the value of the estimated y-intercept.
An auditing firm has developed a set of criteria for determining whether a particular
account (and its balance) is in error. Historically, at companies where the gross sales are
under $25 million, they know that of balances that were in error, 75 percent were
regarded as unusual. Assume Company A shows a history of only 10 percent of the
account balances being in error and it also shows that 25 percent of the account
balances were unusual. What are the states of nature and the experimental outcomes?
An experiment was performed on a certain metal to determine if the strength is a
function of heating time. The sample size consists of 10 metal sheets. The simple linear
regression equation is = 1 + 1X. The time is in minutes and the strength is measured in
pounds per square inch. One of the 10 metal sheets was heated for 4 minutes and the
resulting strength was 6 lb per square inch. Calculate the value of the residual for this
observation.
Consider the following partial analysis of variance table from a randomized block
design with 6 blocks and 4 treatments.
Source Sum of Squares
Treatments 15.93
Blocks 42.09
Error 23.84
Total 81.86
Determine the degrees of freedom for treatments.
A baker must monitor the temperature at which cookies are baked. Too much variation
will cause inconsistency in the texture of the cookies. Past records show that the
variance of the temperatures has been 1.44 degrees. A random sample of 30 batches of
cookies is selected, and the sample variance of the temperature is 4.41 degrees. What is
the 95 percent confidence interval for σ2 at α = .05?
An experiment was performed on a certain metal to determine if the strength is a
function of heating time. Results based on 10 metal sheets are given below. Use the
simple linear regression model.
Determine the value of the F statistic.
Using a 90 percent confidence interval of [−.0076, .0276] for the difference between the
proportions of failures in factory 1 and factory 2, where 1 = .05, 2 = .04, n1 = 500,
and n2 = 2000, can we reject the null hypothesis at α = .10?
A motorcycle manufacturer produces the parts for its vehicles in different locations and
transports them to its plant for assembly. To keep the assembly operations running
efficiently, it is vital that all parts be within specification limits. One important part used
in the assembly is the engine camshaft, and one important quality characteristic is the
case hardness depth. Specifications state that the hardness depth must be between 3.0
mm and 6.0 mm. To investigate the process, the quality control engineer selected 25
daily subgroups of n = 5 and measured the hardness depth. The process yielded a mean
of the means = 4.50 and an average range = 1.01. Is the process capable of meeting the
specifications?
A. Yes
B. No
Suppose that a realtor is interested in comparing the price of midrange homes in two
cities in a midwestern state. She conducts a small survey in the two cities, looking at the
price of midrange homes. Assume equal population variances.
Calculate the pooled estimate of σ2 (rounded to nearest hundred).
