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all of above
(A) A two-sample t-test
(B) A two-sample z-test
(C) A matched pairs t-test
(D) A chi-square goodness-of-fit test
(E) A chi-square test of independence
false
true
false
true
true
Simple linear regression or correlation analysis should be used to analyse the data
This variable is a continuous variable
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For Questions 1 and 2:
A randomized experiment was done by randomly assigning each participant either
to walk for half an hour three times a week or to sit quietly reading a book for half
an hour three times a week. At the end of a year the change in participants' blood
pressure over the year was measured, and the change was compared for the two
groups.
Ql.
This is a randomized experiment rather than an observational study because:
a. Blood pressure was measured at the beginning and end of the study.
b. The two groups were comparedatthe end ofthe study.
c. The participants were randomly assigned to either walk or read, rather than
choosing their own activity.
d. A random sample ofparticipants was used.
Q2. The two treatnents in this study were:
a.
b.
c.
d.
Walking for half an hour three times a week and reading a book for half an hour
three times a week.
Having blood pressure measured at the beginning of the study and having blood
pressure measured at the end of the study.
Walking or reading a book for half an hour three times a week and having blood
pressure measured.
Walking or reading a book for half an hour three times a week and doing nothing.
Questions 3 and 4:
A newspaper article reported that "Children who routinely compete in vigorous after-school
sports on smoggy days are three times more likely to get asthma than their no-athletic peers."
Q3. Of the following, which is the most important additional information that
would be useful before making a decision about participation in school sports?
a. Where was the study conducted?
b. How many students in the study participated in after-school sports?
c. What is the baseline risk for getting asthma?
d. Who funded the study?
Q4. The newspaper also reported that "The number of children in the study
who contacted asthma was relatively small, 265 of 3,535." Which of the
following is representedby 26513535: .075?
a. The overall risk of getting asthma for the children in this study.
b. The baseline risk of getting asthma for the 'hon-athletic peers" in the study.
c. The risk of getting asthma for children in the study who participated in sports.
d. The relative risk of getting asthma for children who routinely participate in
vigorous after-school sports on smoggy days and their non-athletic peers.
Q5: lf.u statistically significant difference in blood pressure change at the end of a year for
the two
activities was found, then:
a. It cannot be concluded that the difference in activity caused a difference in the
change in blood pressure because in the course of a year there
are lots of possible
confounding variables.
Whether or not the differen:: yal caused by the difference in
activity depends on
whar else the participants did during the yeir.
It cannot be concluded that the differenci in activity caused a difference
in the
change in blood pressure b-ecause it might be the oiposite, that people
with high
blood pressure v,vere more likery to read a book than to walk.
It can be conclutled that the difierence in activity caused a difference in
the change
in blood pressurebecause of the way the study was done.
b'
c.
,
d'
Q6' What is one of the distinctions between a population parameter arid a samprl roaiui.r
a' A population parameter is only based on conceptual measuremln6, but a sample
statistic is based on a combination of real and conceptual measurements.
b. A sample statistic changes each time you try to measure it, but a population
parameter remains fi xed.
c. A p8pulation.parameter changes each time you try to measure it, but a sample
statistic remains fixed across samples.
d. The trug value of a sample statistic carl'never be known but the true value of a
population parameter can be known.
Q7: A mTgazineprinted a survey in its monthly issue and asked readers to
and send it in. over 1000 readers did so. This type of sample is
called
a. a cluster sample.
b. a self-selected sample.
e. a stratified sample.
d. a simple random sample.
fill it out
:
Q8' Which ofthe following would be most likely to produce selection bias in a survey?
a. Using questions with biased wording.
b. only receiving responses from half of the people in the sample.
c. conducting interviews by telephone instead oiin person.
d. Using a r-andom sample of students at a universityto estimate the proportion of
people who think the regal diinking age shourd be rowered.
Q9. Which one ofthe following variables is not categorical?
a.
b.
c.
d.
Age of a person.
Gender of a person: male or female.
Choice on a test item: true or false.
Marital status of a person (singre, married, divorced, other)
For Questions 10,
eIl, and el2:
A suryey asked people how often they exceed speed limits.
The data are then categorized into the
following c@table
of counts showin
esponse.
Exceed
Limit if Possible?
Not Always
Total
Under 30
Q10. Anrong people with age over 31,what's the "risk" of always
exceeding the speed limit?
a,
b.
g,
d.
0.20
0.40
0.33
0.50
Ql 1' Among people with age under
a. l to2
-10
what are the odds that they always exceed the
speed limit?
b. 2to l
c. ltol
d.
$ii,y*Xlis
s0%
the relative risk of alwavs exceeding the speed
timit for people under 30 compared to
a.
2.s
b. 0.4
c. 0.5
d. 30%
Q 13. A polling agency conducted a survey of r 00 doctors
on the question ,,Are you
willing to treat women patients with the recentry
upprou"a firi'RU-4g6,,? Th.
conservative margin of error associated wittr
ttre gsi/, confi'dence interval for the
percent who say'yes' is
a. 50yo
b, l0%
c. sYo
d.20h
Ql4' which
one ofthese statistics is unaffected by
outriers?
a. Mean
b. Interquartile range
c. Standard deviation
d.
Range
Ql5. A list of 5 pulse rates is: 70, 64,go,74,92.what
a. 74 b.76 c.77 d. 80
is the median
fbrthis Iist?
Ql6. Which of the following would indicate that
d,
b.
c.
d.
a dataset is not bell-shaped?
The range is equal to 5 standard deviations.
The range is larger than the interquartile range.
The mean is much smaller than the median.
There are no outliers.
Ql7. A scatter plot of number of teachers and number of people with college
degrees for cities in Califomia reveals a positive association. The most likely
explanation for this positive association is:
Teachers excourage people to get college degrees, so an
increase in the number of teachers is causing an increase
in the number of people with college degrees.
Larger cities tend to have both more teachers and more
people with college degrees, so the associhtion is
explained by a third variable, the size of the city.
a,
b.
.
.
c.
Teaching is a common profession for people with college
degrees, so an increase in the number of people with college
degrees causes an increase in the number ofteachers.
fl. Cties with higher incomes tend to have more teachers and
more people going to college, so income is a confounding
variable, making causation between number of teachers and
number ofpeople with college degrees difficult to prove.
Ql8.
The value of a correlation is reported by a researcher to be r =
statements is correct?
-0.5. Which of the following
a. The x-variable exp|ains 25Yo
of the variability in they-variable.
b. The x-variable explains -25% of the variability in they-variable.
c. The x-variable explains 50% of the variability in they-variable.
d. The x-variable explains *50% of the variability in they-variable.
Q19. What is theeffect of an outlier on the value of a correlation coefficient?
a. An outlier will always decrease a correlation coefficient.
b. An outlier will always increase a correlation coefficient.
c. An outlier might either decrease or increase a correlation coeffrcient,
depending on where it is ln relation to the other points.
d. An outlier will have no effect on a correlation coefficient.
For Qaestions Q20, Q2I, and Q22:
A randomized experiment was done by randomly assigning each participant either
to walk for half an hour three times a week or to sit quietly reading a book for half
an hour three times a week. At the end of a year the change in participants' blood
pressure over the year was measured, and the change was compared for the two
$oups.
Q20. This is a randomized experiment rather than an observational study because:
a.
Blood pressure was measured at the beginning and end of the study.
b, The two groups were compared at the end of the study.
c. The partitipants were randomly assigned to either walk or read, rather than
choosing their own activity.
n .
d. A random sample of participants was used.
,
Q2l. The two treatnents in this study were:
a. Walking for half an hour three times a week and reading a book
for half an hour three times a week.
b.
(a..Having blood pressure measured at the beginning ofthe study
and having blood pressure measured at the end of ttre study.
Walking or reading a book for half an hour three times a week
and having blood pressure measured.
d. Walking or reading a book for half an hour three times a week and doing
c.
nothing.
Q22.lf
a statistically significant difference in blood pressure change at the end
of a year for the
nvo activities was found, then:
a. It cannot be concltrded that the difference in activity caused a
difference in the change in blood pressure because in the course
of a year there are lots of possible confounding variables.
b. Whether or not the difference was caused by the difference
in activity depends on what else the participants did during the
,year.
c. It cannot be concluded that the difference in activity caused a
difference in the change in blood pressure because it might be the
opposite, that people with high blood pressure were more likely
to read a book than to walk.
d. It can be concluded that the difference in activity caused a
difference in the change in blood pressure because of the way the
study was done.
Q23. One use of a regression line is
a.
b.
c.
d.
to determine if any x-values are outliers.
to determine if any y-values are outliers.
to determine if a change in x causes a change in y,
to estimate the change in y for a one-unit change in x.
Q24. Past data has shown that the regression line relating the final exam score
and the midterm exam score for students who take statistics from a certain
professor is:
final exam:50 * 0.5 .midterm
One interpretation ofttre slope is
a. a student who scored 0 on the midterm would be predicted to score 50 on
'
the finalexam.
b: a student who scored 0 on the final exam would be predicted
to score 50 on the midterm exam.
c. a student who scored l0 points higher than another student on the midterm
would be prddicted to score 3 points fiigt than the other student on the final
"r
exam.
d. students only receive half as much credit (.5) for a correct
'
answer on the final exam compared to a correct answer on
the midterm exarn.
-
For Questions 25 and Q26:
A study was done tfcompare the lung capacity of coal miners to the lung capacity
of farm workers. The researcher studied 200 workers of each type. Other factors
that might affect lung capacity are smoking habits and exercise habits. The smoking
habits of the two worker types are similar, but the coal miners generally exercise
less than the farm workers.
Q25. Which of the following is the explanatory variable in this study?
a.
Exercise
b. Lung capacity
c.
i
Smoking or not
d. Occupation
Q26. Which of the following is a confounding variable in this study?
. a. Exercise
b. Lung capacity
c. Smoking or not
d. Occupation
it
r.
Q27. Luminous lamps has three factories
- F,, Fz, and Fr with production capacity 30, 50, and 20
units per week respectively. These units are to be shipped to four warehouses W,, Wr, Wr, &nd
W+ with requirement of 20,40, 30, and l0 units per week respectively. The transportation costs (in
Rs.) per unit between factories and warehouses are given below.
Factory
Wr
Fr121430
F2332150
Fs425920
Demand
20
Warehouse
Wz
Ws
Supply
Wl
/-a
40
30
l0
Find an initial basig feasible solution of the given transportation problem using northwest comer
rule
Q28. A company makes two products (X and Y) using two machines (A and B). Each
unit of X that is produced requires 50 minutes processing time on machine A and 30
minutes processing time on machine B. Each unit of Y that is produced requires 24
minutes processing time on machirie A and 33 minutes processing time on machine B.
At the start of the current week there are 30 units of X and 90 units of Y in stock.
Available processing time on machine A is forecast to be 40 hours and on machine B
is forecast to be 35 hours.
The demand for X in the current week is forecast to be 75 units and for Y is forecast
to be 95 units. Company policy is to maximize the combined sum of the units of X
and the units of Y in stock at the end of the week.
.
.
Formulate the problem of deciding how much of each product to make in the
current week as a linear program.
Solve this linear program graphically.
A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles
that move along a filling line. The machine that dispenses salad dressings is working properly
Q29.
when 8 ounces are dispensed. Suppose that the average amount dispensed in a particular sample
of 35 bottles is 7.91 ounces with a variance of 0.03 ounces squared, s2
. Is there evidence that the machine should be stopped and production wait for repairs? The lost
production from a shutdown is potentially so great that management feels that the level
significance in the analysis should be 99%.
of
Q30. In a packaging plant, a machine packs cartons with jars. It is supposed that a new machine
would pack faster on the average than the machine currently used. To test the hypothesis, the time
it takes each machine to pack ten cartons are recorded. The result in ieconds is as follows.
New Machine
42.1
OId Machine
.o
42,7
4t
43,6
41,.3
43.9
4l.g
43.3
42.4
42.5
42.8
43 "5
43 "2
43.1
42.3
4tr,.7
41 .g
44
42.7
44.1
Do the data provide sufficient evidence to conclude that, on the average, the new machine packs
faster? Perform the required hypothesis test at the SYo level of significance.
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What is the purpose of descriptive statistics?
a) To make inferences about a population
b) To summarize and describe data
c) To test hypotheses
d) To establish causation
Two fair six-sided dice are rolled. What is the probability of obtaining a sum of 7 or
a) l/6
b) U3
c) 5ll2
d) t/2
ll?
Which of the following is a measure of central tendency?
a) Standard deviation
b)
c)
d)
4.
Y
0{+.rrlt*^clJ
{e*rl3!
Range
Variance
Median
In a normal distribution, what percentage of the data falls within one standard deviation from
the mean?
a) 25%
b) s0%
c) 68%
5.
6.
7.
d) es%
What is the purpose of inferential statistics?
a) To describe and summarize data
b) To make predictions about future events
c) To draw conclusions and make inferences about a population based on a sample
d) To establish causation
What does a p-value less than 0.05 indicate in hypothesis testing?
a) Strong evidence against the null hypothesis
b) Weak evidence against the null hypothesis
c) No evidence against the null hypothesis
d) Inoonclusive result
What is the difference between a type I and type II error?
a) Type I eror is rejecting a true null hypothesis, while type II error is failing to reject a
b)
c)
d)
false null hypothesis.
Type I eror is failing to reject a true null hypothesis, while type II error is rejecting a
false null hypothesis.
Type I error occurs when the sample size is small, while type II error occurs when the
sample size is large.
Type I error occurs in one-tailed tests, while type II eror occurs in two-tailed tests.
8.
Which statistical test is used to compare the me
ns of two independent groups?
a) Paired t-test
b)
Chi-square test
c) Analysis of variance (ANOVA)
d) Independent t-test
9.
what is the purpose of correlation analysis?
a) To determine causation between two v ables
b) To describe the relationship between tw vari ab le s
c) To compare means of two groups
d) To test hypotheses about proportions
What is the formula for calculating tir. standard
eviation?
a) (sum of values) / (Number of val*es)
b) Square root of the variance
c) (Rang e) / (Number of values)
d) (Median) - (Mean)
11. what is the pu{pose of a confidence
interv al?
a) To estimate the population parameter wi a certain level of confidence
b) To compare two independent groups
c) To test the significance of a difference
een two means
d) To determine the strength of association tween two variables
12' Which statistical test is useO to compare
more th n two means?
a) Independent t-test
b) Chi-square test
c) Analysis of variance (ANOVA)
d) Paired
.
13, what is the purpose of a chi-square test?
a) To compare means of two independent g oups
b) To compare proportions of categorical dr
c) To test the correlation between two conti uous variables
d) To analyze the variance in a dataset
14. What is the difference between a population
and sample?
a) A population refers to the entire set of in ividuals, while a sample is
a subset of
the population,
b) A population refers to a sample that is re resentative of the entire dataset.
c) A population refers to the observed data, hile a sample refers to the
expected
data.
d) A population refers to a sample that is ra
domly selected fiom the entire dataset.
15. What is the purpose of randomization in
a clinic I trial?
a) To ensure that all participants receive
the
e treatment
b) To assign participants to different treatm
t groups without bias
c) To eliminate confounding variables
d) To increase the statistical power of the st
dy
10.
t-test
I
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I
I
I
I
16.
I
which of the foilowing is an example of a cate[oricar variable?
a)
b)
Ase
I
Height
c) Blood pressure
d) Gender
I
I
I
17. What is the purpose of a null hypothesis?
a) To provide an alternative hypothesis forltestine
I
b)
To determine the sample size fbr a studyl
c) To represent the hypothesis of no effect br no difference
d) To describe the characteristics of a popuf ation
18. What is the purpose of a
a) To visualize rhe distribution of a datasetl
b) To compare means of two independent jroups
c) To analyze the variance in a dataset
d) To determine the correration between twb variabres
l9' In a deck of 52 playing cards, what is the proba{ility of drawing
a heart or a queen?
boxplot?
I
I
a) ets2
b) t3ts2
I
c) ts/sz
I
d) t7/s2
I
I
20' which statisticaltest is used to compare propo.tlon, of
categorical data from independent
-
groups?
I
a) Paired t-test
b) Chi-square test
c) Analysis of variance (ANOVA)
d) Independent t-tesr
plot?
I
I
|
I
2l . What is the purpose of a scatter
a) To visualize the relationship between twd continuous variables
b) To compare means of two independent g{oups
c) To analyze the variance in a dataset
d) To determine the correration between twd variabres
22. what is the purpose of a matched pairs design inla stuoyz
a) To compare means of two independent g{oups
b) To compare proportions of categorical Jalra
c) To analyze the variance in a dataset
d) To control for confounding variables
23. What is the purpose of a one_way ANOVA?
a) To compare means of two independent grloups
b) To compare proportions of categorical data
c) To analyze the variance in a dataset with lnore than two srouDs
d) To determine the correlation between tw{ variabres
I
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24. \Nhafis the purpose of a paired
a) To compare means of two independent $roups
b) To compare means of paired observatio{s or repeated measurements
c) To analyze the variance in a dataset
d) To determine the correration between tulo variabres
25' A company has three factories and four wareho{rses. The transportation
costs per unit
from each factory to each warehouse are given the table below. Determine
the optimal
{n
transportation plan to minimize the total cost.
t-test?
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Factory2l6l3lll2l
Factory3l 4l2lsl3l
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26' A furniture manufacturer produces two types or[^u,rr, classic
and Modern. The Classic
chair requires 4 hours of labor and 2 square met{rs of wood, while
the Modern chair
requires 3 hours of labor and 3 square meters of[wood. The
company has 40 hours of
labor and 24 square meters of wood available. Tlre profit per
Classic chair is $30, and the
profit per Modem chair is $25. How many chairi of each type should
the company
produce to maximize
profit?
I
I
27. A box contains 6 red balls and 4 blue balls. Twd balls are drawn at random
with
replacement. what is the probability of getting tfoo blue balls?
(a)
(b)
(c)
(d)
ttz5
t/36
t/16
lit0o
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28. In agroupof 40 students,20 study French, l5 s{udy Spanish, and g study
both
languages. If a student is selected at random, wn{t is the probability
that ihey study at
least one of the two languages?
(a) t/2
(b) 7fi0
(c) ett}
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(d) tsfi6
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29. Solve the following transportation proble. urin! the MoDI method.
The costs per unit
for transportation from each factory to each *u.*f.rorr. are given below:
I
Warehouse
I
I Warehouse
2 | Warfhouse 3
----:-t-----------t--____-____-_l_____-_l
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|
2
, Factory 2l
l
Factory3l
5 |
I
6
3 |
z
5
The supply at each factory and the deman
Supply at Factory
at each warehouse are as follows:
l: 90 units
Supply at Factory Z: I I0 units
Supply at Factory
3
: l2A units
Demand at Warehouse
l: 80 units
Demand at Warehouse
2: I00 units
Demand at Warehouse
3: 140 units
Find the optimal transportation plan and th total cost.
30. A transportation comp any has three routes for d livering goods:
Route I, Route 2, and
Route 3" The transportation costs per unit for ea h route are
$5, $8, and $ 10, respectively.
The demand at each destination is 100 units for oute l, 150 units
for Route Z, and 200
units for Route 3. The company has 300 units a ilable for transport.
How many units
should be transported on each route to minim ize the total transportation
cost?