In an attempt to determine whether or not special training increases the speed with which assembly

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:

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.

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)      (Bonus5 points) Which variables in the current regression model are significant? And which are not significant? Justify your answer.