When one company buys another company, it is not unusual that some workers are t
ID: 3236212 • Letter: W
Question
When one company buys another company, it is not unusual that some workers are terminated. The severance benefits offered to the laid-off workers are often the subject of dispute. Suppose that the Laurier Company recently bought the Western Company and subsequently terminated 20 of Western’s employees. As part of the buyout agreement, it was promised that the severance package offered to the former Western employees would be equivalent to those offered to Laurier employees who had been terminated in the past year. Thirty-six-year-old Bill Smith, a Western employee for the past 10 years, was one of those let go. His severance package included an offer of 5 weeks’ severance pay. Bill complained that this offer was less than that offered to Laurier’s employees when they were laid off, in contravention of the buyout agreement. A statistician was called in to settle the dispute. The statistician was told that severance is determined by length of service with the company. To determine how generous the severance package had been, a random sample of 50 Laurier ex-employees was taken. For each, the following variables were recorded:
Number of weeks of severance pay Number of years with the company
The statistician would like to use the above sample information and the appropriate statistical method to determine whether Bill is correct in his assessment of the severance package.
Include a problem definition, analysis and final conclusion.
All important analysis steps needs to be followed to arrive at the model to be used for prediction.
Your final conclusion should use both the 95% confidence and prediction intervals. Improper use of these and corresponding wrong/sloppy interpretations is highly penalized.
• Use Data Analysis for Regression and then either Data Analysis Plus or the Regression Template for the intervals.
Weeks SP Years 13 16 13 19 11 8 14 16 3 4 10 9 4 3 7 2 Weeks SP Number of weeks of severance pay 12 15 7 15 Years Number of years with the company 8 13 11 10 9 5 10 13 18 19 17 20 13 11 14 19 5 2 11 15 10 14 8 6 15 16 7 6 9 8 11 12 10 13 8 14 5 7 6 4 14 12 12 17 10 11 14 14 12 17 12 17 8 8 12 16 10 10 11 13 15 19 5 6 8 9 11 11 15 15 11 13 6 5 6 7 13 14 9 10Explanation / Answer
Bill should have got a severance pay for 9.36 weeks where as he got it only for 5 weeks. His complaint is valid.
Regression Analysis r² 0.690 n 50 r 0.831 k 1 Std. Error 1.917 Dep. Var. SP Weeks (y) ANOVA table Source SS df MS F p-value Regression 393.2178 1 393.2178 107.00 8.27E-14 Residual 176.4022 48 3.6750 Total 569.6200 49 Regression output confidence interval variables coefficients std. error t (df=48) p-value 95% lower 95% upper std. coeff. Intercept 3.6214 0.000 Service (x) 0.5743 0.0555 10.344 8.27E-14 0.4626 0.6859 0.831 Predicted values for: SP Weeks (y) 95% Confidence Interval 95% Prediction Interval Service (x) Predicted lower upper lower upper Leverage 10 9.364 8.792 9.936 5.467 13.261 0.022Related Questions
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