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 is the unweighted aggregate price index for the basket of
four food items in 2010 using 2008 as the base year?

Accepted Answer

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

Question 2

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 value of MSA is __________, while MSBL is __________.

Accepted Answer

The answer of SCENARIO 11-13
An important factor in selecting database...

Question 3

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 none of the new employees will be from
University A?

Accepted Answer

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

Question 4

SCENARIO 9-12
A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic
the drug company is currently producing has a normal distribution with a mean of 7.4 minutes with a
standard deviation of 1.2 minutes. The chemistry of the new anesthetic is such that the effective time
should be normally distributed with the same standard deviation. The company will market the new
local anesthetic as being better if there is evidence that the population mean effective time is greater
than the 7.4 minutes of the current local anesthetic.
-Referring to Scenario 9-12, if you select a sample of 25 new local anesthetics and are willing to
have a level of significance of 0.1, the confidence coefficient of the test is _____ if the population
mean effective time is 8 minutes.

Accepted Answer

The answer of SCENARIO 9-12
A drug company is considering marketing...

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 Laspeyres price index for the group of three energy
items in year 5 for a family that consumed 15 units of electricity, 24 units of natural gas and
200 units of fuel oil in year 1 using hear 1 as the base year?

Accepted Answer

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

Question 6

SCENARIO 5-12
Two different designs on a new line of winter jackets for the coming winter are available for your
manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers
when winter arrives. The probability of the three possible different tastes of the consumers and the
corresponding profits are presented in the following table. $$\begin{array} { | c | c | r | r | } 
\hline \text { Probability } & \text { Taste } & \text { Design A } & \text { Design B } \
\hline 0.2 & \text { more conservative } & 180 & 520 \
\hline 0.5 & \text { no change } & 230 & 310 \
\hline 0.3 & \text { more liberal } & 350 & 270 \
\hline
\end{array}$$
-Referring to Scenario 5-12, if you decide to choose Design A for 90% of the production lines and
Design B for the remaining production lines, what is the coefficient of variation of your
investment?

Accepted Answer

The answer of SCENARIO 5-12
Two different designs on a new...

Question 7

As a general rule, one can use the normal distribution to approximate a binomial
distribution whenever the sample size is at least 30.

Accepted Answer

A) True 
 B)False

Question 8

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, exactly two of the cars have non-defective radios?

Accepted Answer

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

Question 9

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, in order to perform the test, you need to assume that the
amount filled by the machine follows a normal distribution.

Accepted Answer

A) True 
 B)False

Question 10

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, what is the value of the F test statistic for testing the block effects?

Accepted Answer

The answer of SCENARIO 11-13
An important factor in selecting database...

Question 11

SCENARIO 4-17
Jake woke up late in the morning on the day that he has to go to school to take an important test. He
can either take the shuttle bus which is usually running late 20% of the time or ride his unreliable
motorcycle which breaks down 40% of the time. He decides to toss a fair coin to make his choice.
-Referring to Scenario 4-17, if Jake is late to the test, what is the probability that he rode his bike?

Accepted Answer

The answer of SCENARIO 4-17
Jake woke up late in the...

Question 12

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, exactly half of the cars have defective radios?

Accepted Answer

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

Question 13

SCENARIO 6-7
The interval between consecutive hits at a web site is assumed to follow an exponential distribution
with a mean of 40 hits per minute.
-Referring to Scenario 6-7, what is the mean time between consecutive hits?

Accepted Answer

The answer of SCENARIO 6-7
The interval between consecutive hits at...

Question 14

SCENARIO 9-13
A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production
process is working properly. Based on past experience, the population standard deviation is 50 hours
and the light bulb life is normally distributed. The operations manager stops the production process if
there is evidence that the population mean light bulb life is below 500 hours.
-Referring to Scenario 9-13, if you select a sample of 100 light bulbs and are willing to have a
level of significance of 0.05, the probability of the operations manager stopping the process when
the process is not working properly is _____ if the population mean bulb life is 490 hours.

Accepted Answer

The answer of SCENARIO 9-13
A manufacturer produces light bulbs that...

Question 15

SCENARIO 4-16
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%.
-Referring to Scenario 4-16, if a randomly selected student lives in the dormitory, what is the
probability that the student is a freshman?

Accepted Answer

The answer of SCENARIO 4-16
According to the record of the...

Question 16

As a general rule, one can use the normal distribution to approximate a binomial
distribution whenever the sample size is at least 15.

Accepted Answer

A) True 
 B)False

Question 17

SCENARIO 9-12
A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic
the drug company is currently producing has a normal distribution with a mean of 7.4 minutes with a
standard deviation of 1.2 minutes. The chemistry of the new anesthetic is such that the effective time
should be normally distributed with the same standard deviation. The company will market the new
local anesthetic as being better if there is evidence that the population mean effective time is greater
than the 7.4 minutes of the current local anesthetic.
-Referring to Scenario 9-12, if you select a sample of 25 new local anesthetics and are willing to
have a level of significance of 0.01, the probability of the company not marketing the new local
anesthetic when its population mean effective time is not greater than the 7.4 minutes is _____.

Accepted Answer

The answer of SCENARIO 9-12
A drug company is considering marketing...

Question 18

SCENARIO 12-19
The director of transportation of a large company is interested in the usage of the company's van pool
program. She surveyed 129 of her employees on the usage of the program before and after a
campaign to convince her employees to use the service and obtained the following:  She will use this information to perform test using a level of significance of 0.05.
-Referring to Scenario 12-19, the director now wants to know if the proportion of employees who use the service before the campaign and the proportion of employees who use the service after the
Campaign are the same. Which test should she use?

Accepted Answer

A)  $\chi ^ { 2 }$ -test for difference in proportions 
B)  Z-test for difference in proportions 
C)  McNemar test for difference in proportions 
D)  Wilcoxon rank sum test

Question 19

The covariance

Accepted Answer

A)  must be between -1 and +1. 
B)  must be positive. 
C)  can be positive or negative. 
D)  must be less than +1.

Question 20

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...

Exam 20: Probability and Combinatorics

As a general rule, one can use the normal distribution to approximate a binomial distribution whenever the sample size is at least 30.

SCENARIO 6-7 The interval between consecutive hits at a web site is assumed to follow an exponential distribution with a mean of 40 hits per minute. -Referring to Scenario 6-7, what is the mean time between consecutive hits?

As a general rule, one can use the normal distribution to approximate a binomial distribution whenever the sample size is at least 15.

The covariance