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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 significancea = 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 week’s 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 4–7. Use the 3-day weighted moving average method for forecasting days 4–7. Use Weight 1 day ago = 2, Weight 2 days ago = 4, and Weight 3 days ago = 3. 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. 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).

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 significancea = 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 week’s 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

 

  1. Use the 3-day moving average method for forecasting days 4–7.
  2. Use the 3-day weighted moving average method for forecasting days 4–7. Use Weight 1 day ago = 2, Weight 2 days ago = 4, and Weight 3 days ago = 3.
  3. 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

 

  1. 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.
  2. 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.
  3. 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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