The local police department must write, on average, 5 tickets a day to keep
department revenues at budgeted levels. Suppose the number of tickets
written per day follows a Poisson distribution with a mean of 6.5 tickets
per day. Interpret the value of the mean.
The mean has no interpretation since 0.5 ticket can never be written.
If we sampled all days, the arithmetic average or expected number of
tickets written would be 6.5 tickets per day.
The number of tickets that is written most often is 6.5 tickets per day.
Half of the days have less than 6.5 tickets written and half of the days
have more than 6.5 tickets written.
An airline wants to select a computer software package for its reservation
system. Four software packages (1, 2, 3, and 4) are commercially available.
The airline will choose the package that bumps as few passengers, on the
average, as possible during a month. An experiment is set up in which each
package is used to make reservations for 5 randomly selected weeks. (A
total of 20 weeks was included in the experiment.) The number of
passengers bumped each week is given below. How should the data be
analyzed?
Package 1: 12, 14, 9, 11, 16
Package 2: 2, 4, 7, 3, 1
Package 3: 10, 9, 6, 10, 12
Package 4: 7, 6, 6, 15, 12
F test for differences in variances.
t test for the mean difference.
One-way ANOVA F test.
t test for the differences in means.
A medical doctor is involved in a $1 million malpractice suit. He can either
settle out of court for $250,000 or go to court. If he goes to court and loses,
he must pay $825,000 plus $175,000 in court costs. If he wins in court, the
plaintiffs pay the court costs. Identify the actions of this decision making
problem.
Two choices: (1) go to court and (2) settle out of court.
Four consequences resulting from Go/Settle and Win/Lose combinations.
Two possibilities: (1) win the case in court and (2) lose the case in court.
The amount of money paid by the doctor.
In a binomial distribution
the probability of success p is stable from trial to trial.
the results of one trial are dependent on the results of the other trials.
the number of trials, n , must be at least 30.
the random variable X is continuous.
Since a ________ is not a randomly selected probability sample, there is no
way to know how well it represents the overall population.
quota sample.
simple random sample.
cluster sample.
stratified sample.
An economist is interested in studying the incomes of consumers in a
particular region. The population standard deviation is known to be $1,000.
A random sample of 50 individuals resulted in an average income of
$15,000. What is the upper end point in a 99% confidence interval for the
average income?
$15,141
$15,052
$15,330
$15,364
A major videocassette rental chain is considering opening a new store in an
area that currently does not have any such stores. The chain will open if
there is evidence that more than 5,000 of the 20,000 households in the area
are equipped with videocassette recorders (VCRs). It conducts a telephone
poll of 300 randomly selected households in the area and finds that 96 have
VCRs. The rental chain’s conclusion from the hypothesis test using a 3%
level of significance is
to open a new store.
to delay opening a new store until additional evidence is collected.
not to open a new store.
We cannot tell what the decision should be from the information given.
A multiple-choice test has 30 questions. There are 4 choices for each
question. A student who has not studied for the test decides to answer all
questions randomly. What type of probability distribution can be used to
figure out his chance of getting at least 20 questions right?
Poisson distribution.
binomial distribution.
hypergeometric distribution.
none of the above.
Let X represent the amount of time it takes a student to park in the
library parking lot at the university. If we know that the distribution of
parking times can be modeled using an exponential distribution with a
mean of 4 minutes, find the probability that it will take a randomly
selected student more than 10 minutes to park in the library lot.
0.917915
0.329680
0.670320
0.082085
The owner of a fish market has an assistant who has determined that the
weights of catfish are normally distributed, with mean of 3.2 pounds and
standard deviation of 0.8 pound. What percentage of samples of 4 fish will
have sample means between 3.0 and 4.0 pounds?
16%
67%
84%
29%
Suppose a 95% confidence interval for μ turns out to be (1,000, 2,100). To
make more useful inferences from the data, it is desired to reduce the
width of the confidence interval. Which of the following will result in a
reduced interval width?
Increase the sample size.
Decrease the confidence level.
Both increase the sample size and decrease the confidence level.
Both increase the confidence level and decrease the sample size.
At α = 0.10 , there is sufficient evidence to conclude that the average
number of tissues used during a cold is not 60 tissues.
At α = 0.05 , there is not sufficient evidence to conclude that the
average number of tissues used during a cold is not 60 tissues.
At α = 0.05 , there is not sufficient evidence to conclude that the
average number of tissues used during a cold is 60 tissues.
At α = 0.05 , there is sufficient evidence to conclude that the average
number of tissues used during a cold is 60 tissues.
Testing for the existence of correlation is equivalent to
the confidence interval estimate for predicting Y .
testing for the existence of the Y-intercept (β0 ) .
testing for the existence of the slope (β 1 ) .
none of the above.
A company has 125 personal computers. The probability that any one of them
will require repair on a given day is 0.15.
Referring to the above information, which of the following is one of the
properties required so that the binomial distribution can be used to
compute the probability that no more than 2 computers will require repair
on a given day?
The probability that any one of the computers that will require repair
on a given day will not affect or change the probability that any other
computers that will require repair on the same day.
The probability that two or more computers that will require repair in a
given day approaches zero.
The probability that a computer that will require repair in the morning
is the same as that in the afternoon.
The number of computers that will require repair in the morning is
independent of the number of computers that will require repair in the
afternoon.
Referring to the above information, the researcher was attempting to show
statistically that the female MBA graduates have a significantly lower
mean starting salary than the male MBA graduates. According to the test
run, which of the following is an appropriate alternative hypothesis?
H1 : μfemales ≠ μmales
H1 : μfemales < μmales
H1 : μfemales = μmales
H1 : μfemales > μmales
A quality control engineer is in charge of the manufacture of computer disks.
Two different processes can be used to manufacture the disks. He suspects that
the Kohler method produces a greater proportion of defects than the Russell
method. He samples 150 of the Kohler and 200 of the Russell disks and finds
that 27 and 18 of them, respectively, are defective. If Kohler is designated as
“Group 1” and Russell is designated as “Group 2,” perform the appropriate test
at a level of significance of 0.01.
Referring to the above information, the hypotheses that should be tested
are:
H0 :π1 −π 2 ≥ 0 vs. H1 :π1 −π2 < 0
H0 :π1 −π 2 =0 vs. H1 :π1 −π2 ≠ 0
H0 :π1 −π 2 ≠ 0 vs. H1 :π1 −π2 =0
H0 :π1 −π 2 ≤ 0 vs. H1 :π1 −π2 >0
Psychologists have found that people are generally reluctant to transmit bad
news to their peers. This phenomenon has been termed the “MUM effect.” To
investigate the cause of the MUM effect, 40 undergraduates at Duke
University participated in an experiment. Each subject was asked to
administer an IQ test to another student and then provide the test taker with
his or her percentile score. Unknown to the subject, the test taker was a bogus
student who was working with the researchers. The experimenters
manipulated two factors: subject visibility and success of test taker, each at two
levels. Subject visibility was either visible or not visible to the test taker.
Success of the test take was either visible or not visible to the test taker.
Success of the test taker was either top 20% or bottom 20%. Ten subjects were
randomly assigned to each of the 2×2 = 4 experimental conditions, then the
time (in seconds) between the end of the test and the delivery of the percentile
score from the subject to the test taker was measured. (This variable is called
the latency to feedback.) The data were subjected to appropriate analyses with
the following results.
Referring to the above information, in the context of this study, interpret
the statement: “Subject visibility and test taker success interact.”
The relationship between feedback time and subject visibility depends
on the success of the test taker.
The difference between the mean feedback time for test takers scoring
in the top 20% and bottom 20% depends on the visibility of the subject.
The difference between the mean feedback time for visible and
nonvisible subjects depends on the success of the test taker.
All of the above are correct interpretations.
We are 95% confident that average service charge (Y ) will increase
between $15 and $30 for every $1 million increase in sales revenue
(X) .
At the α = 0.05 level, there is no evidence of a linear relationship
between service charge (Y ) and sales revenue (X) .
We are 95% confident that the mean service charge will fall between
$15 and $30 per month.
We are 95% confident that the sales revenue (X) will increase
between $15 and $30 million for every $1 increase in service charge
(Y ) .
Referring to the above information, to test whether aggregate price index
has a positive impact on consumption, the p-value is:
0.8330
0.5835
0.0001
0.4165
Referring to the above information, what is the p-value for testing whether
Wages have a positive impact on corporate sales?
0.00005
0.01
0.0001
0.05
According to the record of the registrar’s office at a state university, 35% of
the students are freshman, 25% are sophomore, 16% are junior and the
rest are senior. Among the freshmen, sophomores, juniors and seniors, the
portion of students who live in the dormitory are, respectively, 80%, 60%,
30% and 20%.
(a) determine whether the class status of a student and whether the
student lives in a dormitory are statistically independent.
(b) what percentage of the students live in a dormitory?
Patients arriving at an outpatient clinic follow an exponential distribution
with a mean of 15 minutes. What is the probability that a randomly chosen
arrival would be more than 18 minutes?
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