# STAS3001

Solve the following statistical business problems. You must show your work to get full marks. For all problems were an alpha is required use alpha=.05.

Please put your work in the STAS3001 FINAL EXAM Dropbox under the assignments tab in blackboard.

Question 1 (4 marks)

An HR department wanted to know if workers productivity drops on Fridays. An HR analyst randomly selects 5 workers and measures their productivity output on Wednesday and then again on Friday.

Worker Wed Output Friday Output

1 71 53

2 56 47

3 75 52

4 68 55

5 74 58

using an alpha of .05 to see if there is evidence to suggest that productivity falls on Friday. Assume the difference in productivity is normally distributed.

Question 2 (5 marks)

A national car company was concerned that customer age and region affected the speed of repair service received. A survey was conducted in various regions and age groups asking them to rate the speed of repair service on a 7 point scale, with 1 being the slowest and 7 being the fastest service. Assuming the data is normal distributed, conduct the proper ANOVA and interpret the results. Use alpha=.05.

Question 3 (6 marks)

A financial analyst wishes to predict business revenue using cost, product price index and a consumer confidence index as possible predictors. He calculated two models, one using cost, product price index and consumer confidence index as predictors and one using only two interaction variables of cost x product price index and product price index x consumer confidence index to predict revenue. Generate both of these models and interpret the excel output. Use the equation of the strongest model to predict revenue for year 7.

Question 4 (8 marks)

Following are the average yields of long-term new corporate bonds over a 12 month period;

Month Yield

10.08

10.05

9.24

9.23

Calculate forecast values for each the 12 months using the following 4 forecast methods:

Simple average

4 month moving average

Simple exponential smoothing with alpha=.3

Simple exponential smoothing with alpha=.7

Which model produces the better forecast and why?

Question 5 (5 marks)

A company wants to determine if the sales of 6 cookie flavours are uniformly distributing so they know if they should continue to produce the same amount of each cookie in their factory. Random sales data was collected over 6 months and showed the following sales results measured in boxes of cookies sold:

Question 6 (6 marks)

A new store in a mall was trying to determine if customer arrivals to their store match the poisson distribution to help staff appropriately. They gathered data in one-minute intervals from 6:30pm to 8:00pm and obtained the following results.

Arrivals per Minute Observed Frequency

26

40

using an alpha=.05 determine if customer store arrivals match the poisson distribution on this non-parametric data.

Question 7 (5 marks)

An HR department wanted to determine if job type is independent of years working in the computer science industry. The HR analysts collected the following non-parametric categorical data:

Manager

Programmer

Operator

Systems Analyst

0-3

6

37

11

13

Years Worked

4-8

28

16

23

24

8

47

10

12

19

use excel to interpret if job type is independent of years worked. use alpha =.05

Question 8 (4 marks)

use the Wilcoxon matched-pairs signed rank test to determine whether there is a significant difference between the related populations below. Use alpha=.05.

Group1 Group2

5.6 6.4

1.3 1.5

4.7 4.6

3.8 4.3

2.4 2.1

5.5 6.0

5.1 5.2

4.6 4.5

3.7 4.5

Please put your work in the STAS3001 FINAL EXAM Dropbox under the assignments tab in blackboard.

Question 1 (4 marks)

An HR department wanted to know if workers productivity drops on Fridays. An HR analyst randomly selects 5 workers and measures their productivity output on Wednesday and then again on Friday.

Worker Wed Output Friday Output

1 71 53

2 56 47

3 75 52

4 68 55

5 74 58

using an alpha of .05 to see if there is evidence to suggest that productivity falls on Friday. Assume the difference in productivity is normally distributed.

Question 2 (5 marks)

A national car company was concerned that customer age and region affected the speed of repair service received. A survey was conducted in various regions and age groups asking them to rate the speed of repair service on a 7 point scale, with 1 being the slowest and 7 being the fastest service. Assuming the data is normal distributed, conduct the proper ANOVA and interpret the results. Use alpha=.05.

Question 3 (6 marks)

A financial analyst wishes to predict business revenue using cost, product price index and a consumer confidence index as possible predictors. He calculated two models, one using cost, product price index and consumer confidence index as predictors and one using only two interaction variables of cost x product price index and product price index x consumer confidence index to predict revenue. Generate both of these models and interpret the excel output. Use the equation of the strongest model to predict revenue for year 7.

Question 4 (8 marks)

Following are the average yields of long-term new corporate bonds over a 12 month period;

Month Yield

10.08

10.05

9.24

9.23

Calculate forecast values for each the 12 months using the following 4 forecast methods:

Simple average

4 month moving average

Simple exponential smoothing with alpha=.3

Simple exponential smoothing with alpha=.7

Which model produces the better forecast and why?

Question 5 (5 marks)

A company wants to determine if the sales of 6 cookie flavours are uniformly distributing so they know if they should continue to produce the same amount of each cookie in their factory. Random sales data was collected over 6 months and showed the following sales results measured in boxes of cookies sold:

Question 6 (6 marks)

A new store in a mall was trying to determine if customer arrivals to their store match the poisson distribution to help staff appropriately. They gathered data in one-minute intervals from 6:30pm to 8:00pm and obtained the following results.

Arrivals per Minute Observed Frequency

26

40

using an alpha=.05 determine if customer store arrivals match the poisson distribution on this non-parametric data.

Question 7 (5 marks)

An HR department wanted to determine if job type is independent of years working in the computer science industry. The HR analysts collected the following non-parametric categorical data:

Manager

Programmer

Operator

Systems Analyst

0-3

6

37

11

13

Years Worked

4-8

28

16

23

24

8

47

10

12

19

use excel to interpret if job type is independent of years worked. use alpha =.05

Question 8 (4 marks)

use the Wilcoxon matched-pairs signed rank test to determine whether there is a significant difference between the related populations below. Use alpha=.05.

Group1 Group2

5.6 6.4

1.3 1.5

4.7 4.6

3.8 4.3

2.4 2.1

5.5 6.0

5.1 5.2

4.6 4.5

3.7 4.5

You'll get a 1.1MB .ZIP file.