Question 1

SCENARIO 16-17
Given below are the prices of a basket of four food items from 2008 to 2012. $$\begin{array} { c r r r r } 
\hline \text { Year } & \text { Wheat(\$/Bushel) } & \text { Corn(\$/Bushel) } & \text { Soybeans(\$/Bushel) } & \text { Milk(\$/hundredweight) } \
\hline 2008 & 4.25 & 3.71 & 7.41 & 15.03 \
2009 & 3.43 & 2.7 & 7.55 & 13.63 \
2010 & 2.63 & 2.3 & 6.05 & 15.18 \
2011 & 2.11 & 1.97 & 4.68 & 14.72 \
2012 & 2.16 & 1.9 & 4.81 & 12.32
\end{array}$$
-Referring to Scenario 16-17, what are the simple price indices for wheat, corn, soybeans and
milk, respectively, in 2011 using 2008 as the base year?

Accepted Answer

The answer of SCENARIO 16-17
Given below are the prices of...

Question 2

SCENARIO 5-11
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition. The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution: 
-Referring to Scenario 5-11, if you can invest 30% of your money on the house in neighborhood A
and the remaining on the house in neighborhood B, what is the portfolio expected return of your
investment?

Accepted Answer

The answer of SCENARIO 5-11
There are two houses with almost...

Question 3

The number of resamples is irrelevant in constructing a bootstrap confidence
interval estimate for the population mean.

Accepted Answer

A) True 
 B)False

Question 4

A stock analyst was provided with a list of 25 stocks. He was expected to pick 3 stocks from the list whose prices are expected to rise by more than 20% after 30 days. In reality, the prices of
Only 5 stocks would rise by more than 20% after 30 days. If he randomly selected 3 stocks from
The list, he would use what type of probability distribution to compute the probability that all of
The chosen stocks would appreciate more than 20% after 30 days?

Accepted Answer

A)  binomial distribution. 
B)  Poisson distribution. 
C)  hypergeometric distribution. 
D)  none of the above.

Question 5

SCENARIO 16-16
Given below are the average prices for three types of energy products for five consecutive years. $$\begin{array} { r r r r } 
\text { Year } & \text { Electricity } & \text { Natural Gas } & \text { Fuel Oil } \
1 & 43.205 & 25.893 & 0.892 \
2 & 16.959 & 28.749 & 0.969 \
3 & 47.202 & 28.933 & 1.034 \
4 & 48.874 & 29.872 & 0.913 \
5 & 48.693 & 28.384 & 0.983
\end{array}$$
-Referring to Scenario 16-16, , what is the unweighted aggregate price index for the group of
three energy items in year 5 using year 1 as the base year?

Accepted Answer

The answer of SCENARIO 16-16
Given below are the average prices...

Question 6

Bootstrapping is used to construct an interval estimate for the population mean
when you cannot assume that the population is normally distributed and the sample size is not
large enough to apply the Central Limit Theorem.

Accepted Answer

A) True 
 B)False

Question 7

SCENARIO 11-12
A student team in a business statistics course designed an experiment to investigate whether the brand
of bubblegum used affected the size of bubbles they could blow. To reduce the person-to-person
variability, the students decided to use a randomized block design using themselves as blocks.
Four brands of bubblegum were tested. A student chewed two pieces of a brand of gum and then blew
a bubble, attempting to make it as big as possible. Another student measured the diameter of the
bubble at its biggest point. The following table gives the diameters of the bubbles (in inches) for the
16 observations. 
-Referring to Scenario 11-12, the value of MSA is __________, while MSBL is __________.

Accepted Answer

The answer of SCENARIO 11-12
A student team in a business...

Question 8

To construct a bootstrap confidence interval estimate for the population mean, you
will order the resampled means for the m samples that you have drawn from the initial sample of
size n, use the value of the resampled mean that cuts off the smallest α/ 2×100% as the lower
limit and the value of that cuts off the largest α/ 2×100% as the upper limit.

Accepted Answer

A) True 
 B)False

Question 9

SCENARIO 11-11
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants all 3
varieties of the seeds on each of 5 different patches of fields. She then measures the crop yield in
bushels per acre. Treating this as a randomized block design, the results are presented in the table that
follows. $\begin{array}{rrrr}
\underline {\text { Fields }} &\underline {\text { Smith}}&  \underline{\text {Walsh}}&  \underline{\text {Trevor }}\
1&11.1 & 19.0 & 14.6 \
2&13.5 & 18.0 & 15.7 \
3&15.3 & 19.8 & 16.8 \
4&14.6 & 19.6 & 16.7 \
5&9.8 & 16.6 & 15.2
\end{array}$
-Referring to Scenario 11-11, the randomized block F test is valid only if there is no
interaction between the variety of seeds and the patches of fields.

Accepted Answer

A) True 
 B)False

Question 10

SCENARIO 9-11
An appliance manufacturer claims to have developed a compact microwave oven that consumes a
population mean of no more than 250 W. From previous studies, it is believed that power
consumption for microwave ovens is normally distributed with a population standard deviation of 15
W. If there is evidence that the population mean consumption is greater than 250 W, the manufacturer
will be unable to make the claim.
-Referring to Scenario 9-11, if you select a sample of 20 compact microwave ovens and are
willing to have a level of significance of 0.01, the probability of making a Type II error is _____
if the mean power consumption of all such microwave ovens is in fact 248 W.

Accepted Answer

The answer of SCENARIO 9-11
An appliance manufacturer claims to have...

Question 11

SCENARIO 11-13
An important factor in selecting database software is the time required for a user to learn how to use
the system. To evaluate three potential brands (A, B and C) of database software, a company
designed a test involving five different employees. To reduce variability due to differences among
employees, each of the five employees is trained on each of the three different brands. The amount of
time (in hours) needed to learn each of the three different brands is given below: $\begin{array}{ | r | r | r | r | }

\hline & & \text { Software } & \
\hline \text { Operator } & \text { A } & \text { B } & \text { C } \
\hline 1 & 17 & 17 & 23 \
\hline 2 & 18 & 17 & 23 \
\hline 3 & 14 & 13 & 19 \
\hline 4 & 12 & 11 & 18 \
\hline 5 & 19 & 17 & 22 \
\hline \text { Mean } & 16 & 15 & 21 \
\hline
\end{array}$

$\text { Below is the Excel output for the randomized block design: }$
$\begin{array}{lrrrrrr}
\hline \text { Source of Variation } & S S & d f & \text { MS } & {\text { F }} & \text { P-value } & \text { Fcrit } \
\hline \text { Rows } & 84.66667 & 4 & 21.16667 & 50.8 & 9.98 \mathrm{E}-06 & 3.837853 \
\text { Columns } & 103.3333 & 2 & 51.66667 & 124 & 9.54 \mathrm{E}-07 & 4.45897 \
\text { Error } & 3.333333 & 8 & 0.416667 & & & \
\text { Total } & 191.3333 & 14 & & & & \
\hline
\end{array}$ 
-Referring to Scenario 11-13, the randomized block F test is valid only if the
population of the amount of time needed is normally distributed for the 3 brands.

Accepted Answer

A) True 
 B)False

Question 12

SCENARIO 11-11
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants all 3
varieties of the seeds on each of 5 different patches of fields. She then measures the crop yield in
bushels per acre. Treating this as a randomized block design, the results are presented in the table that
follows. $\begin{array}{rrrr}
\underline {\text { Fields }} &\underline {\text { Smith}}&  \underline{\text {Walsh}}&  \underline{\text {Trevor }}\
1&11.1 & 19.0 & 14.6 \
2&13.5 & 18.0 & 15.7 \
3&15.3 & 19.8 & 16.8 \
4&14.6 & 19.6 & 16.7 \
5&9.8 & 16.6 & 15.2
\end{array}$
-Referring to Scenario 11-11, the null hypothesis for the randomized block F test
for the difference in the means should be rejected at a 0.01 level of significance.

Accepted Answer

A) True 
 B)False

Question 13

SCENARIO 12-21
A filling machine at a local soft drinks company is calibrated to fill the cans at a mean amount of 12
fluid ounces and a standard deviation of 0.5 ounces. The company wants to test whether the standard
deviation of the amount filled by the machine is 0.5 ounces. A random sample of 15 cans filled by
the machine reveals a standard deviation of 0.67 ounces.
-Referring to Scenario 12-21, what are the lower and upper critical values of the test when
allowing for 5% probability of committing a type I error?

Accepted Answer

The answer of SCENARIO 12-21
A filling machine at a local...

Question 14

The expected return of the sum of two investments will be equal to the sum of the
expected returns of the two investments plus twice the covariance between the investments.

Accepted Answer

A) True 
 B)False

Question 15

SCENARIO 11-11
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants all 3
varieties of the seeds on each of 5 different patches of fields. She then measures the crop yield in
bushels per acre. Treating this as a randomized block design, the results are presented in the table that
follows. $\begin{array}{rrrr}
\underline {\text { Fields }} &\underline {\text { Smith}}&  \underline{\text {Walsh}}&  \underline{\text {Trevor }}\
1&11.1 & 19.0 & 14.6 \
2&13.5 & 18.0 & 15.7 \
3&15.3 & 19.8 & 16.8 \
4&14.6 & 19.6 & 16.7 \
5&9.8 & 16.6 & 15.2
\end{array}$
-Referring to Scenario 11-11, what is the critical value of the randomized block F test for the
difference in the means at a level of significance of 0.01?

Accepted Answer

The answer of SCENARIO 11-11
An agronomist wants to compare the...

Question 16

SCENARIO 5-14
An accounting firm in a college town usually recruits employees from two of the universities in town.
This year, there are fifteen graduates from University A and five from University B and the firm
decides to hire six new employees from the two universities.
-Referring to Scenario 5-14, what is the probability that more than four of the new employees will
be from University A?

Accepted Answer

The answer of SCENARIO 5-14
An accounting firm in a college...

Question 17

SCENARIO 5-13
From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that
12 have defective radios installed.
-Referring to Scenario 5-13, what is the probability out of the 8 new cars it just received that,
when each is tested, no more than 2 of the cars have defective radios?

Accepted Answer

The answer of SCENARIO 5-13
From an inventory of 48 new...

Question 18

The O in the DCOVA framework stands for "organize".

Accepted Answer

A) True 
 B)False

Question 19

The interval between patients arriving at an outpatient clinic follows an exponential distribution
at a rate of 1 patient per hour. What is the probability that a randomly chosen arrival to be
more than 1 hour?

Accepted Answer

The answer of The interval between patients arriving at an...

Question 20

A new model car from Ford Motor Company offers a keyless entry system that utilizes a four-
letter code. How many different possible combinations are there for the code?

Accepted Answer

The answer of A new model car from Ford Motor...

Exam 20: Probability and Combinatorics

The number of resamples is irrelevant in constructing a bootstrap confidence interval estimate for the population mean.

Bootstrapping is used to construct an interval estimate for the population mean when you cannot assume that the population is normally distributed and the sample size is not large enough to apply the Central Limit Theorem.

The expected return of the sum of two investments will be equal to the sum of the expected returns of the two investments plus twice the covariance between the investments.

The O in the DCOVA framework stands for "organize".

The interval between patients arriving at an outpatient clinic follows an exponential distribution at a rate of 1 patient per hour. What is the probability that a randomly chosen arrival to be more than 1 hour?

A new model car from Ford Motor Company offers a keyless entry system that utilizes a four- letter code. How many different possible combinations are there for the code?