QSO 510 Quantitative Analysis Midterm Exam SPRING 2014

Problem 3. (20 points)In an attempt to determine whether or not special training increases the speed with whichassembly line workers can do an assembly job at AMTEL Inc., 25 workers are timed performingthe task. Then, they are given a special training course designed to increases their assemblyefficiency. At the end of the course, they are timed doing the same task. The differences betweenthe first and the second time are recorded for each of the 25 assembly line workers. The meanimprovement for the 25 workers was found to be 2.6 minutes and the sample standard deviationwas 4 minutes.Let variable represents the improvement in time for each assembly line worker. Let representsthe average improvement in time for the population. Has the training improved the time requiredon the job? Please test the hypothesis use as the level of significance. (Hint: meaning that thetraining 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 BoysAppliances over the past two years:TimeSales2010 Quarter 1252010 Quarter 2852010 Quarter 3642010 Quarter 4302011 Quarter 1702011 Quarter 21252011 Quarter 31052011 Quarter 490The scatter plot of the data above shows seasonality with trend. Hence, a multiple regressionmodel 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 independentvariables. Here, we choose quarter 1 as the baseline and adopt three seasonality dummyvariables, such that represents quarter 2, represents quarter 3, and represents quarter 4. Answerthe following questions. Usea) (5 points) Use the above variable definition to code the data above.TimeSales(Y)Time (t)2010 Quarter 12512010 Quarter 28522010 Quarter 36432010 Quarter 43042011 Quarter 17052011 Quarter 212562011 Quarter 310572011 Quarter 4908b) (5 points) Copy the data into Excel and run the corresponding multiple regression. Write theestimated multiple regression equation use the variables defined above. (Hint: No need toconduct 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 rightcontext.)d) (5 points) Test the overall fitness of the model. (State the hypotheses, and use Significant Fto complete your test.)e) (Bonus 5 points) Which variables in the current regression model are significant? And whichare not significant? Justify your answer.