QSO 510 Final Exam

Directions:

This exam consists of 5 problems and is an open-book exam with no time limit. All

work should be done individually. Word-process your solutions within this

template and show all steps used in arriving at the final answers. Incomplete

solutions will receive partial credit. Copy and paste all necessary data from

Excel into this document and create tables as needed.

Problem 1

Suppose a manufacturing

company makes a certain item. The time to produce each item is normally

distributed around a mean of 27 minutes with a standard deviation of 2.5

minutes. Thus, the population of production times is normal in shape. Find the

mean and standard deviation of the sample.

Sample size is 100.

Problem 2

The

average prices for a product in 12 stores in a city are shown below.

$2.99, $2.85, $3.25, $3.55, $3.00, $2.99,

$2.76, $3.50, $3.20, $2.85, $3.75, $3.85

Test

the hypothesis that the average price is higher than $2.87. Use level of

significance a

= 0.05.

Problem

3

A store wishes to predict net profit as

a function of sales for the next year. The following table gives the years 1998

to 2005.

Year

Sales

(thousands

of dollars)

Net

Profit

1998

51

5

1999

55

10.2

2000

65

9.6

2001

82

-3

2002

75

2.8

2003

71

3.2

2004

82

-2.3

2005

81

-2.6

(a) Graph

the points from 1998 through 2005 on a scatter diagram using Sales as the

independent variable and Net Profit as the dependent variable.

(b) Draw

the regression line on the graph you constructed in Part (a).

(c) What

is the value of the coefficient of determination for this regression model?

Comment on the strength of the regression line for this model.

(d) What

is the predicted net profit for 2006 if sales are expected to be 125?

Problem 4

Last

weekâs sales of iMac computers at an Apple Store in Oklahoma City, OK, are

shown in the following table:

Day

Sales

(Dollars)

1

180

2

150

3

210

4

225

5

195

6

190

7

230

Use the 3-day moving average method for

forecasting days 4â7..25in;’=”” list=”” lfo1;=””>Use

the 3-day weighted moving average method for forecasting days 4â7. Use Weight 1

day ago = 2, Weight 2 days ago = 4, and Weight 3 days ago = 3..25in;’=”” list=”” lfo1;=””>Compare

the techniques using the mean absolute deviation (MAD).Problem

5

The following table shows six years of average annual cost-of-living

index data:

Year

Annual Cost of Living Index

2005

98.2

2006

101.3

2007

103.7

2008

105.8

2009

111.4

2010

121.9

2011

134.3

2012

128.6

2013

125.2

Forecast the average annual cost

of living index for all years from 2008 to 2013. Use a 3-year weighted moving

average with weights of 0.5, 0.3, and 0.2. Use the largest weight with the most

recent data.Forecast the average annual cost

of living index using exponential smoothing with ? = 0.7 for all years

from 2008 to 2014. Use the rate for 2008 as the starting forecast for 2008.Here,Which of the methods in

parts (a) and (b) produces better forecasts for the 3 years from 2011 to 2013?

Answer on the basis of mean square error (MAD).

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