Deck 28: Using Statistics for Decision Making

Question 1

Use the following to answer the question(s) below.
The monthly returns on a social choice portfolio comprised of "green" companies are shown below for the last six months of 2007.
Month Monthly Return
July 2.2 %
August 2.5
September 1.8
October 1.4
November 1.1
December 1.9
The forecasted monthly return for January 2008 using a three-month moving average is

A) 2.8
B) 1.9
C) 2.0
D) 2.4
E) 1.5

Answer 1

E

Question 2

The expected value of perfect information is

A) $590
B) -$250
C) $1290
D) $700
E) -$450

Answer 2

D

Question 3

Machine oil is used by clothing manufacturers to lubricate and protect sewing machines. A company that produces machine oil must ensure that the viscosity of its product meets customer requirements. Consequently, the viscosity of every batch of oil produced is measured. Suppose that the process mean is 101 cP and the process standard deviation is 1.50 cP. What is the Cpk index if the customer specifications require viscosity of the machine oil to be 100 cP ± 4.5 cP?

A) 1.0
B) 1.22
C) 0.78
D) 1.67
E) 1.28

Answer 3

C

Question 4

What is the expected value of perfect information?

A) $326.25
B) $310
C) $535
D) $208.75
E) $225

Question 5

The standard deviations (in thousands of dollars) for building a small and large complex are 535 and 976, respectively. Based on the resulting coefficients of variation (CV), which of the following statements would be true?

A) The CV of building a large complex is less than that of building a small complex.
B) The CV of building a small complex is less than that of building a large complex.
C) The risk averse action would be to build a large complex.
D) The CV of building a large complex is less than that of building a small complex and the risk averse action would be to build a large complex.
E) The CV of building a small complex is less than that of building a large complex and the risk averse action would be to build a large complex.

Question 6

A producer of specialty products uses a variety of natural and man-made materials to make unique countertops for kitchens and baths. One product line mixes concrete and natural river stone to make countertops that are polished to a high shine revealing unique patterns. Occasionally coarse sand will result in undesirable pitting and rough spots on surfaces. Consequently, as part of its quality control efforts, 8 by 4 metre polished slabs are checked periodically for imperfections. For each slab inspected the number of imperfections (pits, rough spots, etc.) is recorded. What type of control chart should be used for these data?

A) Individuals chart
B) p-chart
C) c-chart
D) x-bar and R charts
E) ARL chart

Question 7

Machine oil is used by clothing manufacturers to lubricate and protect sewing machines. A company that produces machine oil must ensure that the viscosity of its product meets customer requirements. Consequently, the viscosity of every batch of oil produced is measured. Suppose that the process mean is 101 cP and the process standard deviation is 1.50 cP. What type of chart should be used to ensure the process remains in control?

A) p-chart
B) c-chart
C) R-chart
D) Chart for individual observations (run chart)
E) ARL chart

Question 8

By design, a required dimension on a part is 0.575 cm plus or minus 0.008 cm. Assume that the process producing this part is stable with a mean of 0.579 cm and standard deviation of 0.002 cm. What is the Cp index?

A) 1.33
B) 2.00
C) 0.67
D) 1.00
E) 0.33

Question 9

Use the following to answer the question(s) below.
The time series graph below shows annual sales figures (in thousands of dollars) for a well known department store chain.
Which model would be most appropriate for forecasting this series?

A) Moving Average
B) Single Exponential Smoothing
C) Quadratic Trend
D) Linear Trend
E) Seasonal Regression

Question 10

Use the following to answer the question(s) below.
Sunny Side Condominiums recently purchased land outside of Toronto and is trying to decide the size complex it should build (large or small). The following payoff table (in thousands of dollars) considers three possible levels of demand.
Using the maximax approach, Sunny Side should

A) build a small complex
B) build a large complex
C) build a large complex with high demand
D) build a small complex with low demand
E) not build any size complex

Question 11

Use the following to answer the question(s) below.
Sunny Side Condominiums recently purchased land outside of Toronto and is trying to decide the size complex it should build (large or small). The following payoff table (in thousands of dollars) considers three possible levels of demand.
If there is a 45% chance that the demand level will be low, 30% that it will be medium and 25% chance that it will be high, the expected value (in thousands of dollars) associated with the best action is

A) $326.25
B) $310
C) $535
D) $208.75
E) $225

Question 12

Use the following to answer the question below.
The time series graph below shows monthly sales figures for a specialty gift item sold on the Home Shopping Network (HSN).
The dominant time series component in these data is

A) Cyclical
B) Seasonal
C) Randomness
D) Irregular
E) Error

Question 13

Use the following to answer the question(s) below.
As a result of the financial crisis in the fall of 2008, where the government intervened to help the economy, an investor was considering various strategies for her money and the estimated profits would depend on how successful the intervention would be in helping the economy. The estimated annual return for two different investment strategies are shown in the following table.
If there is a 30% chance that the economy will decline, 50% that there will be no change and 20% chance that it will rebound, the expected value associated with the best investment strategy is

A) $590
B) -$250
C) $1290
D) $700
E) -$450

Question 14

Quarterly returns were forecasted for a mutual fund made up of technology stocks. The forecast errors for the last six quarters are as follows: -0.47, 1.12, -0.85, 1.27, 0.07, and -0.05. The MAD based on these forecast errors is

A) 0.77
B) 0.98
C) 0.22
D) 0.18
E) 0.64

Question 15

Use the following to answer the question(s) below.
The monthly returns on a social choice portfolio comprised of "green" companies are shown below for the last six months of 2007.
Month Monthly Return
July 2.2 %
August 2.5
September 1.8
October 1.4
November 1.1
December 1.9
Use a single exponential smoothing (SES) model with α = 0.8 to forecast for January 2008. Assume that the forecast for December 2007 was 1.18 %.

A) 1.50
B) 1.18
C) 1.76
D) 1.90
E) 2.20

Question 16

The standard deviation associated with the investment strategy of allocating 80% to stocks and 20% to bonds is

A) $4,500
B) $2,250
C) $3,473
D) $2,567
E) $1,782

Question 17

Use the following to answer the question(s) below.
As a result of the financial crisis in the fall of 2008, where the government intervened to help the economy, an investor was considering various strategies for her money and the estimated profits would depend on how successful the intervention would be in helping the economy. The estimated annual return for two different investment strategies are shown in the following table.
Using the maximax approach, the investor should

A) choose 20% stocks 80% bonds
B) choose 80% stocks 20% bonds
C) choose 20% stocks 80% bonds if the economy rebounds
D) choose 80% stocks 20% bonds if the economy declines
E) put her money in her mattress

Question 18

The minimax choice

A) minimizes the maximum cost
B) maximizes the minimum cost
C) minimizes the maximum profit
D) minimizes the maximum revenue
E) can be any of the given answers

Question 19

Use the following to answer the question(s) below.
The time series graph below shows annual sales figures (in thousands of dollars) for a well known department store chain.
The dominant time series component in these data is

A) Trend
B) Seasonal
C) Randomness
D) Irregular
E) Error

Question 20

Machine oil is used by clothing manufacturers to lubricate and protect sewing machines. A company that produces machine oil must ensure that the viscosity of its product meets customer requirements. Consequently, the viscosity of every batch of oil produced is measured. Suppose that the process mean is 101 cP and the process standard deviation is 1.50 cP. What are the limits for a runs chart to be used to see that the process remains control?

A) 99.5 cP and 102.5 cP
B) 96.5 cP and 105.5 cP
C) 95.5 cP and 106.5 cP
D) 92.5 cP and 110.5 cP
E) 99.5 cP and 107.5 cP

Question 21

A producer of specialty products uses a variety of natural and man-made materials to make unique countertops for kitchens and baths. One product line mixes concrete and natural river stone to make countertops that are polished to a high shine revealing unique patterns. Occasionally coarse sand will result in undesirable pitting and rough spots on surfaces. Consequently, as part of its quality control efforts, 8 by 4 metre polished slabs are checked periodically for imperfections. For each slab inspected the number of imperfections (pits, rough spots, etc.) is recorded. If the average number of imperfections per 8 by 4 metre polished slab is 2.6, the control limits for the appropriate control chart are

A) 0 and 7.44
B) 0.98 and 4.21
C) 0 and 9.89
D) 1.24 and 3.96
E) 1.24 and 4.21

Question 22

An automatic filling process is used to dispense hand sanitizer into small purse size bottles. The target weight is 75 ml. The company has initiated control charting to stabilize and improve the automatic filling process. For each of twenty-five samples consisting of four bottles, the contents were measured and the mean weight and range were determined. The average of the means across all samples was found to be 72.5 ml. and the average range was 2.75 ml. The control limits for the R chart are

A) 0 and 4.3566 ml
B) 0 and 6.2755 ml
C) 0 and 2.8875 ml
D) 2.00 and 3.50 ml
E) 2.00 and 4.3566 ml

Question 23

An automatic filling process is used to dispense hand sanitizer into small purse size bottles. The target weight is 75 ml. The company has initiated control charting to stabilize and improve the automatic filling process. For each of twenty-five samples consisting of four bottles, the contents were measured and the mean weight and range were determined. The average of the means across all samples was found to be 72.5 ml. and the average range was 2.75 ml. The estimate of the process standard deviation is

A) 2.75 ml
B) 2.44 ml
C) 1.88 ml
D) 1.34 ml
E) Indeterminate

Question 24

An automatic filling process is used to dispense hand sanitizer into small purse size bottles. The target weight is 75 ml. The company has initiated control charting to stabilize and improve the automatic filling process. For each of twenty-five samples consisting of four bottles, the contents were measured and the mean weight and range were determined. The average of the means across all samples was found to be 72.5 ml. and the average range was 2.75 ml. The control limits for the x-bar chart are

A) 68.48 and 76.52 ml
B) 71.16 and 73.84 ml
C) 70.49 and 74.51 ml
D) 72 and 73 ml
E) 68.48 and 74.51 ml

Question 25

In order to achieve higher levels of customer satisfaction, a company begins monitoring the complaint resolution process of its customer service representatives. As a first step, the company decides to collect data on the number of unanswered calls out of the first 250 incoming calls to its call centre made each day. At the end of monitoring 25 days, it was found that a total of 500 incoming calls went unanswered. The control limits for the p-chart of these data are

A) 0.029 and 0.131
B) 0 and 0.304
C) 0.066 and 0.094
D) 0.048 and 0.112
E) 0.029 and 0.112

Question 26

The minimin choice strategy is

A) the action that minimizes the minimum possible returns across all states of nature
B) the action that minimizes the maximum possible cost across all states of nature
C) the action that minimizes the minimum possible cost across all states of nature
D) the action that maximizes the minimum possible cost across all states of nature
E) the action that maximizes the minimum possible returns across all states of nature