HOLMES INSTITUTE FACULTY OF HIGHER EDUCATION HI6007 Group Assignment Due End of Week 10 WORTH 30% (Maximum 5 students in the group)

MS Excel must be used to perform any calculations/graphical presentations as required in this assignment

Question 1 7 marks

Below you are given the examination scores of 20 students (data set also provided in accompanying MS Excel file).

52 99 92 86 84

63 72 76 95 88

92 58 65 79 80

90 75 74 56 99

a. Construct a frequency distribution, cumulative frequency distribution, relative frequency distribution, cumulative relative frequency distribution and percent frequency distribution for the data set using a class width of 10. (5 marks)

b. Construct a histogram showing the percent frequency distribution of the examination scores. Comment on the shape of the distribution. (2 marks)

Question 2 8 marks

Shown below is a portion of a computer output for a regression analysis relating supply (Y in thousands of units) and unit price (X in thousands of dollars).

ANOVA

df SS

Regression 1 354.689

Residual 39 7035.262

Coefficients Standard Error Intercept 54.076 2.358

X 0.029 0.021

a. What has been the sample size for this problem? (1 mark)

b. Determine whether or not supply and unit price are related. Use a = 0.05. (2 marks)

Compute the coefficient of determination and fully interpret its meaning. Be very specific. c.

(2 marks)

Compute the coefficient of correlation and explain the relationship between supply and

d. unit price. (2 marks)

e. Predict the supply (in units) when the unit price is $50,000. (1 mark) Question 3 6 marks

Allied Corporation wants to increase the productivity of its line workers. Four different programs have been suggested to help increase productivity. Twenty employees, making up a sample, have been randomly assigned to one of the four programs and their output for a day's work has been recorded. You are given the results below (data set also provided in accompanying MS Excel file).

Program A Program B Program C Program D

150 150 185 175

130 120 220 150

120 135 190 120

180 160 180 130

145 110 175 175

a. Construct an ANOVA table. (3 marks)

b. As the statistical consultant to Allied, what would you advise them? Use a .05 level of

significance. (3 marks)

Question 4 9 marks

A company has recorded data on the weekly sales for its product (y), the unit price of the competitor's product (x1), and advertising expenditures (x2). The data resulting from a random sample of 7 weeks follows. Use Excel's Regression Tool to answer the following questions (data set also provided in accompanying MS Excel file).

Week Price Advertising Sales

1 .33 5 20

2 .25 2 14

3 .44 7 22

4 .40 9 21

5 .35 4 16

6 .39 8 19

7 .29 9 15

a. What is the estimated regression equation? Show the regression output. (2 marks)

b. Determine whether the model is significant overall. Use a = 0.10. (2 marks)

c. Determine if competitor’s price and advertising is individually significantly related to

sales. Use a = 0.10. (2 marks)

Based on your answer to part (c), drop any insignificant independent variable(s) and d.

re-estimate the model. What is the new estimated regression equation? (2 marks)

e. Interpret the slope coefficient(s) of the model from part (d). (1 marks)

MS Excel must be used to perform any calculations/graphical presentations as required in this assignment

Question 1 7 marks

Below you are given the examination scores of 20 students (data set also provided in accompanying MS Excel file).

52 99 92 86 84

63 72 76 95 88

92 58 65 79 80

90 75 74 56 99

a. Construct a frequency distribution, cumulative frequency distribution, relative frequency distribution, cumulative relative frequency distribution and percent frequency distribution for the data set using a class width of 10. (5 marks)

b. Construct a histogram showing the percent frequency distribution of the examination scores. Comment on the shape of the distribution. (2 marks)

Question 2 8 marks

Shown below is a portion of a computer output for a regression analysis relating supply (Y in thousands of units) and unit price (X in thousands of dollars).

ANOVA

df SS

Regression 1 354.689

Residual 39 7035.262

Coefficients Standard Error Intercept 54.076 2.358

X 0.029 0.021

a. What has been the sample size for this problem? (1 mark)

b. Determine whether or not supply and unit price are related. Use a = 0.05. (2 marks)

Compute the coefficient of determination and fully interpret its meaning. Be very specific. c.

(2 marks)

Compute the coefficient of correlation and explain the relationship between supply and

d. unit price. (2 marks)

e. Predict the supply (in units) when the unit price is $50,000. (1 mark) Question 3 6 marks

Allied Corporation wants to increase the productivity of its line workers. Four different programs have been suggested to help increase productivity. Twenty employees, making up a sample, have been randomly assigned to one of the four programs and their output for a day's work has been recorded. You are given the results below (data set also provided in accompanying MS Excel file).

Program A Program B Program C Program D

150 150 185 175

130 120 220 150

120 135 190 120

180 160 180 130

145 110 175 175

a. Construct an ANOVA table. (3 marks)

b. As the statistical consultant to Allied, what would you advise them? Use a .05 level of

significance. (3 marks)

Question 4 9 marks

A company has recorded data on the weekly sales for its product (y), the unit price of the competitor's product (x1), and advertising expenditures (x2). The data resulting from a random sample of 7 weeks follows. Use Excel's Regression Tool to answer the following questions (data set also provided in accompanying MS Excel file).

Week Price Advertising Sales

1 .33 5 20

2 .25 2 14

3 .44 7 22

4 .40 9 21

5 .35 4 16

6 .39 8 19

7 .29 9 15

a. What is the estimated regression equation? Show the regression output. (2 marks)

b. Determine whether the model is significant overall. Use a = 0.10. (2 marks)

c. Determine if competitor’s price and advertising is individually significantly related to

sales. Use a = 0.10. (2 marks)

Based on your answer to part (c), drop any insignificant independent variable(s) and d.

re-estimate the model. What is the new estimated regression equation? (2 marks)

e. Interpret the slope coefficient(s) of the model from part (d). (1 marks)

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