QSO 510 Quantitative Analysis Midterm Exam SPRING 2013

Problem 3. (20 points)
In an attempt to determine whether or not special training increases the speed with which
assembly line workers can do an assembly job at AMTEL Inc., 25 workers are timed performing
the task. Then, they are given a special training course designed to increases their assembly
efficiency. At the end of the course, they are timed doing the same task. The differences between
the first and the second time are recorded for each of the 25 assembly line workers. The mean
improvement for the 25 workers was found to be 2.6 minutes and the sample standard deviation
was 4 minutes.
Let variable represents the improvement in time for each assembly line worker. Let represents
the average improvement in time for the population. Has the training improved the time required
on the job? Please test the hypothesis use as the level of significance. (Hint: meaning that the
training improves the time. Please follow the 7 step procedure!)

Problem 4. (20 points)
Consider the following time series data representing quarterly sales of dishwashers at Big Boys
Appliances over the past two years:
Time

Sales

2010 Quarter 1

25

2010 Quarter 2

85

2010 Quarter 3

64

2010 Quarter 4

30

2011 Quarter 1

70

2011 Quarter 2

125

2011 Quarter 3

105

2011 Quarter 4

90

The scatter plot of the data above shows seasonality with trend. Hence, a multiple regression
model is run to forecast the demand. We denote sales (Y) as the depend variable, and denote time
(t, with represent the first quarter of 2010) and dummy variables (, , and ) as independent
variables. Here, we choose quarter 1 as the baseline and adopt three seasonality dummy
variables, such that represents quarter 2, represents quarter 3, and represents quarter 4. Answer
the following questions. Use
a) (5 points) Use the above variable definition to code the data above.
Time

Sales(Y)

Time (t)

2010 Quarter 1

25

1

2010 Quarter 2

85

2

2010 Quarter 3

64

3

2010 Quarter 4

30

4

2011 Quarter 1

70

5

2011 Quarter 2

125

6

2011 Quarter 3

105

7

2011 Quarter 4

90

8

b) (5 points) Copy the data into Excel and run the corresponding multiple regression. Write the
estimated multiple regression equation use the variables defined above. (Hint: No need to
conduct backwards elimination at this point.)

c) (5 points) Explain the meaning of the slopes for seasonally dummy variable , , and . (Note:
Use actual variable name and numbers to answer the questions. Put numbers in the right
context.)

d) (5 points) Test the overall fitness of the model. (State the hypotheses, and use Significant F
to complete your test.)

e) (Bonus 5 points) Which variables in the current regression model are significant? And which
are not significant? Justify your answer.