Question

Hi,

For Problem: Severance Pay below.

Please explain why the correct answer is: (1) Between 9 weeks and 10 weeks (for Question: To make sure that the company pays comparable severance pay on the average, Bill Smith's severance pay should be? )

and (2) What is your conclusion? Does Bill deserve more in severance pay?

Thanks

Problem: Severance Pay

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 the 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.

Weeks SP	Years (x)
13	16
13	19
11	8
14	16
3	4
10	9
4	3
7	2
12	15
7	15
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	10

Answer 1

Statistician want to estimate the severance based on the length of the service.

The linear model he used in this case is No.of weeks SP = a+b* ( length of the service)

The regression output for the data of given 50 observations is

The regression equation is
Weeks SP = 3.62 + 0.574 Years

Predictor Coef SE Coef T P
Constant 3.6214 0.6967 5.20 0.000
Years 0.57428 0.05552 10.34 0.000

S = 1.91704 R-Sq = 69.0% R-Sq(adj) = 68.4%

The regression equation is

Weeks SP = 3.62 + 0.574 Years

By substituting the value of X =10 , the predicted severance is SP=9.364

Computation for 95% confidence interval

Intermediate Calculations
Sample Size	50
Degrees of Freedom	48
t Value	2.010635
XBar, Sample Mean of X	11.56
Sum of Squared Differences from XBar	1192.32
Standard Error of the Estimate	1.917041
h Statistic	0.022041
Predicted Y (YHat)	9.36413
For Average Y
Interval Half Width	0.572243
Confidence Interval Lower Limit	8.791887
Confidence Interval Upper Limit	9.936374

The 95% confidence interval is = 8.79, 9.94

For Bill smith, he used the 95% confidence interval of the Laurier ex-employees irrespective of the length of the service.

The 95% confidence of interval of Laurier ex-employees (sample of 50)

Data
Sample Standard Deviation	3.40953046
Sample Mean	10.26
Sample Size	50
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	0.482180422
Degrees of Freedom	49
t Value	2.009575199
Interval Half Width	0.968977817
Confidence Interval
Interval Lower Limit	9.29
Interval Upper Limit	11.23

The 95% confidence interval is 9.29 to 11.23

The statistician estimate is in between 8 to 10 weeks where as Bill estimate is somewhare between 9 to 11.5 weeks.

Bill was paid only for 5 weeks of pay

So Bill argument is valid