A report in a consumer magazine indicated that with 90 percent confidence, the mean
number of hours that a particular brand light bulb lasts is between 900 and 1,100 hours.
Based on this, the sample mean that produced this estimate is 1,000 hours.
A study was recently conducted in which people were asked to indicate which news
medium was their preferred choice for national news. The following data were
observed:
Given this data, if we wish to test whether the preferred news source is independent of
age with an alpha equal to .05, the critical value will be a chi-square value with 9
degrees of freedom.
The Mann-Whitney U test is always a one-tailed test.
Six food critics each visited and rated four different restaurants. Each critic visited each
restaurant on three separate occasions and recorded a score for each visit. The number
of degrees of freedom in the interaction row of the ANOVA table is 15.
A confidence interval will contain the true population value as long as the point
estimate is within the lower to upper limits.
In a contingency analysis, we expect the actual frequencies in each cell to
approximately match the corresponding expected cell frequencies when H0 is true.
Choosing an alpha of 0.01 will cause beta to equal 0.99.
A seafood shop sells salmon fillets where the weight of each fillet is normally
distributed with a mean of 1.6 pounds and a standard deviation of 0.3 pounds. They
want to classify the largest fillets as extra large and charge a higher price for them. If
they want the largest 15 percent of the fillets to be classified as extra large, the
minimum weight for an extra large fillet should be 1.91 pounds.
Six food critics each visited and rated four different restaurants. Each critic visited each
restaurant on three separate occasions and recorded a score for each visit. The critical
value for testing whether there is any difference among the four restaurants, using the
0.05 level of significance is approximately F = 2.8.
If a population is normally distributed, then the sampling distribution for the sample
mean will always be normally distributed regardless of the sample size.
The Adams Shoe Company believes that the mean size for men’s shoes is now more
than 10 inches. To test this, it has selected a random sample of n = 100 men. Assuming
that the test is to be conducted using a .05 level of significance, a p-value of .07 would
lead the company to conclude that its belief is correct.
Suppose 10 students are enrolled in a class and the probability of at least 8 showing up
on a given day is 90 percent. Then the probability of 7 or fewer showing that day is 10
percent.
A stable process is typically defined as one in which all output is operating within 3
standard deviations of the process center.
One of the most common sources of common cause variation is the people who are
working in the process.
The following regression model has been computed based on a sample of twenty
observations: = 34.2 + 19.3x. The first observations in the sample for y and x were
300 and 18, respectively. Given this, the residual value for the first observation is
approximately 81.6.
The t-distribution is still applicable even when there are small violations of the
assumptions for the case when the variances for two populations are unknown. This is
particularly true when the sample sizes are approximately equal.
The Gilbert Company chief financial officer has been tracking annual sales for each of
the company’s three divisions for the past 10 years. At a recent meeting, he pointed to
the annual data and indicated that it clearly showed the seasonality associated with its
business. Given the data, this statement may have been very appropriate.
In a second-order polynomial regression model, the regression coefficient, B2, will be
positive if the parabola opens downward and negative when the parabola opens upward.
The probability of a Type II error decreases as the “true” population value gets farther
from the hypothesized population value, given that everything else is held constant.
Each week American Stores receives a shipment from a supplier. The contract specifies
that the maximum allowable percent defective is 5 percent. When the shipment arrives,
a sample of 20 parts is randomly selected. If 2 or more of the sampled parts are
defective, the shipment is rejected and returned to the supplier. Assume that a shipment
arrives that actually has 4 percent defective parts and the distribution of defective parts
is described by a binomial distribution. The probability that the shipment is accepted is
approximately 0.81
The impact on the margin of error for a confidence interval for an increase in
confidence level and a decrease in sample size is unknown since these changes are
contradictory.
It is possible for the standard error of the estimate to actually increase if variables are
added to the model that do not aid in explaining the variation in the dependent variable.
The forward selection method and the backward elimination method will always lead to
choosing the same final regression model.
When an interviewer asks a specified series of questions in the course of a personal
interview, he/she is conducting an unstructured interview.
To calculate beta requires making a “what if” assumption about the true population
parameter, where the “what-if” value is one that would cause the null hypothesis to be
false.
A joint frequency distribution is used to describe the number of occurrences where two
observations in a data set have the same value.
A study was recently done in the United States in which car owners were asked to
indicate whether their most recent car purchase was a U.S. car, a German car, or a
Japanese car. The people in the survey were divided by geographic region in the United
States. The following data were recorded.
Given this situation, to test whether the car origin is independent of the geographical
location of the buyer, the expected number of people in the sample who bought a
German made car and who lived on the East Coast is just under 40 people.
The number of defects manufactured by workers in a small engine plant is an example
of a discrete random variable.
On a survey there is a question that asks whether someone lives in a house, apartment,
or condominium. These three responses could be coded in a dummy variable using
value 0, 1, and 2.
Experimental design is a plan for performing an experiment where the effects of one or
more factors on the variable of interest are measured.
A business with 5 copy machines keeps track of how many copy machines need service
on a given day. It believes this is binomially distributed with a probability of p = 0.2 of
each machine needing service on any given day. It has collected the following based on
a random sample of 100 days.
Given this information the expected number of days on which exactly 1 machine breaks
down is 40.96.
One of the basic differences between a uniform probability distribution and a normal
probability distribution is that the uniform is symmetrical but the normal is skewed
depending on the value of the standard deviation.
In curvilinear regression modeling, a composite model is one that contains either the
basic terms or the interactive terms but not both.
Process control charts are used to provide signals to indicate when the output of a
process is out of control.
A major airline has stated in an industry report that its mean onground time between
domestic flights is less than 18 minutes. To test this, the company plans to sample 36
randomly selected flights and use a significance level of 0.10. Assuming that the
population standard deviation is known to be 4.0 minutes, the probability that the null
hypothesis will be “accepted” if the true population mean is 16 minutes is
approximately 0.955.
In a study of employees at a local company, the human resource manager wants to
develop a multiple regression model to explain the difference in employee wage rates.
She is thinking of including a variable, degree status, in which the following categories
exist: no degree, H.S. degree, junior college degree, bachelor degree, graduate degree.
Two other variables are being considered; Age and Years With the Company. Given
this, the appropriate number of variables in the model will be six.
The standard error of the estimate is a term that is used for the standard deviation of the
residuals in a multiple regression model.
In the best subsets approach to regression analysis, if we start with 4 independent
variables, a total of 33 different regression models will actually be computed for
possible selection as the best model to use.
There is no difference between cumulative frequency and relative frequency.
Dell Computers receives large shipments of microprocessors from Intel Corp. It must
try to ensure the proportion of microprocessors that are defective is small. Suppose Dell
decides to test five microprocessors out of a shipment of thousands of these
microprocessors. Suppose that if at least one of the microprocessors is defective, the
shipment is returned.
If Intel Corp.’s shipment contains 10% defective microprocessors, calculate the
probability the entire shipment will be returned.
A) 0.4980
B) 0.4209
C) 0.4095
D) 0.4550
It is assumed that the time customers spend in a record store is uniformly distributed
between 3 and 12 minutes. Based on this information, what is the probability that a
customer will spend more than 9 minutes in the record store?
A) 0.33
B) 0.1111
C) 0.67
D) 0.25
The reason for using the t-distribution in a hypothesis test about the population mean is:
A) the population standard deviation is unknown.
B) it results in a lower probability of a Type I error occurring.
C) it provides a smaller critical value than the standard normal distribution for a given
sample size.
D) the population is not normally distributed.
A political poll that is used to indicate the percentage of voters who will vote for a
particular candidate makes use of which of the following?
A) Hypothesis testing
B) Numerical analysis
C) Estimation
D) Both B and C
The editors of a national automotive magazine recently studied 30 different automobiles
sold in the United States with the intent of seeing whether they could develop a multiple
regression model to explain the variation in highway miles per gallon. A number of
different independent variables were collected. The following regression output (with
some values missing) was recently presented to the editors by the magazine’s analysts:
Based on this output and your understanding of multiple regression analysis, which of
the following statements is true?
A) The overall multiple regression model explains a significant portion of the variation
in highway mileage when tested at a significance level of 0.05.
B) Only the two independent variables are statistically significant in the presence of the
others when a significance level of 0.05 is used to test.
C) The standard error of the estimate is a negative value due to the multicollinearity
problems in the model.
D) None of the above is true.
The Russet Potato Company has been working on the development of a new potato
seed that is hoped to be an improvement over the existing seed that is being used.
Specifically, the company hopes that the new seed will result in less variability in
individual potato length than the existing seed without reducing the mean length. To test
whether this is the case, a sample of each seed is used to grow potatoes to maturity. The
following information is given:
The on these data, if the hypothesis test is conducted using a 0.05 level of significance,
the calculated test statistic is:
A) = 1.25
B) = 0.80
C) = 0.64
D) = 1.56
Micron Technology has sales offices located in four cities: Dallas, Seattle, Boston, and
Los Angeles. An analysis of the company’s accounts receivables reveals the number of
overdue invoices by days, as shown here.
Assume the invoices are stored and managed from a central database.
If a randomly selected invoice is from the Los Angeles office, what is the probability
that it is 60 or fewer days overdue?
A) 0.2702
B) 0.0231
C) 0.3461
D) 0.7765
The purpose of a pilot sample is:
A) to provide a better idea of what the population mean will be.
B) to help clarify how the sampling process will be performed.
C) to provide an idea of what the population standard deviation might be.
D) to save time and money instead of having to carry out a full sampling plan.
The following probability distribution has been assessed for the number of accidents
that occur in a Midwestern city each day:
The probability of having less than 2 accidents on a given day is:
A) 0.30
B) 0.75
C) 0.45
D) 0.25
The following data reflect the number of customers who return merchandise for a
refund on Monday. Note these data reflect the population of all 10 Mondays for which
data are available.
Based on these data, what is the standard deviation?
A) 13.03
B) 12.36
C) 39
D) 152.8
The Vardon Exploration Company is getting ready to leave for South America to
explore for oil. One piece of equipment requires 10 batteries that must operate for more
than 2 hours. The batteries being used have a 15 percent chance of failing within 2
hours. The exploration leader plans to take 15 batteries. Assuming that the conditions of
the binomial apply, the probability that the supply of batteries will not contain enough
good ones to operate the equipment is:
A) 0.0449
B) 0.0132
C) 0.9832
D) 0.0168
The transportation manager for the State of New Jersey has determined that the time
between arrivals at a toll booth on the state’s turnpike is exponentially distributed with λ
= 4 cars per minute. Based on this information, what is the probability that the time
between any two cars arriving will exceed 11 seconds?
A) Approximately 1.0
B) Approximately 0.48
C) About 0.52
D) About 0.75
In Excel, what procedure is used to select random numbers?
A) The random numbers function
B) Click on the Data tab, then click on Data Analysis, then click on Sampling
C) Click on the Data tab, then click on Data Analysis, then click on Random Number
Generation
D) Random numbers are not available in Excel.
The manager of a movie theater has determined that the distribution of customers
arriving at the concession stand is Poisson distributed with a standard deviation equal to
2 people per 10 minutes. What is the probability that more than 3 customers arrive
during a 10-minute period?
A) 0.1804
B) 0.5665
C) 0.4335
D) 0.1954
Suppose nine items are randomly sampled from a normally distributed population with
a mean of 100 and a standard deviation of 20. The nine randomly sampled values are:
Calculate the probability of getting a sample mean that is smaller than the sample mean
for these nine sampled values.
A) 0.1411
B) 0.1612
C) 0.1512
D) 0.2266
The undergraduate students at your university are classified as freshmen, sophomores,
juniors, or seniors. A recent study of undergraduates asked the students to indicate the
number of credits they were registered for this term. The responses were 3, 6, 9, 12, 15,
and 18. The number of cells in a joint frequency distribution for the two variables, class
standing, and credit hours is:
A) 4.
B) 10.
C) 24.
D) None of the above.
There are a number of highly touted search engines for finding things of interest on the
Internet. Recently, a consumer rating system ranked two search engines ahead of the
others. Now, a computer user’s magazine wishes to make the final determination
regarding which one is actually better at finding particular information. To do this, each
search engine was used in an attempt to locate specific information using specified
keywords. Both search engines were subjected to 100 queries. Search engine 1
successfully located the information 88 times and search engine 2 located the
information 80 times. Using a significance level equal to 0.05, what is the critical value
for the hypothesis test?
A) z = 196
B) z = 1.645
C) t = 2.0456
D) z = 2.575
Harrison Water Sports has three retail outlets: Seattle, Portland, and Phoenix. The
Seattle store does 50 percent of the total sales in a year, while the Portland store does 35
percent of the total sales. Further analysis indicates that of the sales in Seattle, 20
percent are in boat accessories. The percentage of boat accessories at the Portland store
is 30 and the percentage at the Phoenix store is 25. If a sales dollar is recorded as a boat
accessory, the probability that the sale was made at the Portland store is:
A) slightly greater than 0.43
B) 0.35
C) 0.2425
D) None of the above
Which of the following statements is not consistent with the Central Limit Theorem?
A) The Central Limit Theorem applies without regard to the size of the sample.
B) The Central Limit Theorem applies to non-normal distributions.
C) The Central Limit Theorem indicates that the sampling distribution will be
approximately normal when the sample size is sufficiently large.
D) The Central Limit Theorem indicates that the mean of the sampling distribution will
be equal to the population mean.
Some stores and restaurants have “tell us what you think” cards available for customers.
Assuming that angry customers are more likely to take the time to fill these out, this is
an example of:
A) simple random sampling.
B) stratified sampling.
C) cluster sampling.
D) nonstatistical sampling.
Given a population where the proportion of items with a desired attribute is p = 0.25, if
a sample of 400 is taken, what is the standard deviation of the sampling distribution of
?
A) 0.0512
B) 0.0312
C) 0.0217
D) 0.0412
At a recent meeting, the manager of a national call center for a major Internet bank
made the statement that the average past-due amount for customers who have been
called previously about their bills is now no larger than $20.00. Other bank managers at
the meeting suggested that this statement may be in error and that it might be
worthwhile to conduct a test to see if there is statistical support for the call center
manager’s statement. The file called Bank Call Center contains data for a random
sample of 67 customers from the call center population. Assuming that the population
standard deviation for past due amounts is known to be $60.00, what should be
concluded based on the sample data? Test using α = 0.10.
A) Because p-value = 0.4121 > alpha = 0.10, we do not reject the null hypothesis.
The sample data do not provide sufficient evidence to reject the call center manager’s
statement that the mean past due amount is $20.00 or less.
B) Because p-value = 0.4121 > alpha = 0.10, we reject the null hypothesis.
The sample data provide sufficient evidence to reject the call center manager’s
statement that the mean past due amount is $20.00 or less.
C) Because p-value = 0.2546 > alpha = 0.10, we do not reject the null hypothesis.
The sample data do not provide sufficient evidence to reject the call center manager’s
statement that the mean past due amount is $20.00 or less.
D) Because p-value = 0.2546 > alpha = 0.10, we reject the null hypothesis.
The sample data provide sufficient evidence to reject the call center manager’s
statement that the mean past due amount is $20.00 or less.
A golf ball manufacturer has three dimple patterns it is interested in analyzing to see
whether one results in longer driving distances. However, it also wishes to control for
the cover material the ball is made from since it believes that the material might affect
driving distance. Four materials can be used. The following data represent the results of
tests in which each combination of dimple pattern and cover material were used and the
length of the ball hit by a robot has been recorded. The test will be conducted using an
alpha = 0.05 level.
Given these data, which of the following statements is true?
A) There is no basis for concluding that mean driving distance is different for the
different dimple patterns.
B) There is no basis for concluding that mean driving distance is different for the
different cover materials.
C) Both A and B are true.
D) Neither A nor B is true.
The State Department of Weights and Measures is responsible for making sure that
commercial weighing and measuring devices, such as scales, are accurate so customers
and businesses are not cheated. Periodically, employees of the department go to
businesses and test their scales. For example, a dairy bottles milk in 1-gallon containers.
Suppose that if the filling process is working correctly, the mean volume of all gallon
containers is 1.00 gallon with a standard deviation equal to 0.10 gallon. The
department’s test process requires that they select a random sample of n = 9 containers.
If the sample mean is less than 0.97 gallon, the department will fine the dairy. Based on
this information, suppose that the dairy wants no more than a 0.05 chance of being
fined, which of the following options exist if they can’t alter the filling standard
deviation?
A) They can convince the state to decrease the sample size.
B) They can change the mean fill level to approximately 1.025 gallons.
C) They could lower the mean fill level to a level lower than 1 gallon.
D) There is actually nothing that they can do if they can’t modify the standard deviation.
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, which of the following statements is true?
A) If beta is changed to 0.20 and alpha remains at 0.20, the MAD for periods 2-12 is
reduced.
B) If beta is changed to 0.20 and alpha remains at 0.20, the forecast for period 13 is
slightly reduced.
C) The forecast bias for periods 2-12 is approximately 6.18.
D) All of the above are true.
A multiple regression is shown for a data set of yachts where the dependent variable is
the price in thousands of dollars.
Given this information, which of the following is true regarding the slope coefficient for
Age, where Age represents how many years old the yacht is?
A) On average the price of the yacht falls by $1.778 per year.
B) On average the yacht is 1.778 years older per $1000 price change.
C) On average the price of the yacht falls by $1778 per year.
D) On average the price of the yacht increases by $1778 per year.
A test is conducted to compare three different income tax software packages to
determine whether there is any difference in the average time it takes to prepare income
tax returns using the three different software packages. Ten different person’s income
tax returns are done by each of the three software packages and the time is recorded for
each. Given this format and testing using an alpha level equal to 0.05, the critical value
associated with the primary hypothesis test is:
A) 3.555
B) 2.456
C) 19.385
D) 4.256
Given the following null and alternative hypotheses
H0 : μ1 ≥ μ2
HA : μ1 < μ2
Together with the following sample information
Assuming that the populations are normally distributed with equal variances, test at the
0.05 level of significance whether you would reject the null hypothesis based on the
sample information. Use the test statistic approach.
A) Because the calculated value of t = -2.145 is less than the critical value of t =
-1.6973, reject the null hypothesis. Based on these sample data, at the α = 0.05 level of
significance there is sufficient evidence to conclude that the mean for population 1 is
less than the mean for population 2.
B) Because the calculated value of t = -1.814 is less than the critical value of t =
-1.6973, reject the null hypothesis. Based on these sample data, at the α = 0.05 level of
significance there is sufficient evidence to conclude that the mean for population 1 is
less than the mean for population 2.
C) Because the calculated value of t = -1.329 is not less than the critical value of t =
-1.6973, do not reject the null hypothesis. Based on these sample data, at the α = 0.05
level of significance there is not sufficient evidence to conclude that the mean for
population 1 is less than the mean for population 2.
D) Because the calculated value of t = -1.415 is not less than the critical value of t =
-1.6973, do not reject the null hypothesis. Based on these sample data, at the α = 0.05
level of significance there is not sufficient evidence to conclude that the mean for
population 1 is less than the mean for population 2.
The National Association of Realtors released a survey indicating that a surprising 43%
of first-time home buyers purchased their homes with no-money-down loans during
2005. The fear is that house prices will decline and leave homeowners owing more than
their homes are worth. PMI Mortgage Insurance estimated that there existed a 50% risk
that prices would decline within two years in major metro areas such as San Diego,
Boston, Long Island, New York City, Los Angeles, and San Francisco. A survey taken
by realtors in the San Francisco area found that 12 out of the 20 first-time home buyers
sampled purchased their home with no-money-down loans. Calculate the probability
that at least 12 in a sample of 20 first-time buyers would take out no-money-down loans
if San Francisco’s proportion is the same as the nationwide proportion of
no-money-down loans.
A) 0.0618
B) 0.0124
C) 0.0512
D) 0.0441
For the normal distribution with parameters μ = 5, σ = 4; calculate P(0 < x < 8).
A) 0.8841
B) 0.8812
C) 0.4215
D) 0.6678
If we are performing a two-tailed test of whether μ = 100, the probability of detecting a
shift of the mean to 105 will be ________ the probability of detecting a shift of the
mean to 110.
A) less than
B) greater than
C) equal to
D) not comparable to