Question

1. An experiment was conducted to test the effect of different lighting systems and the presence or absence of a watchman on the average number of car burglaries per month at a parking garage. The data are in the following table and also in the file GARAGE, where the variables are named BURGLAR, LIGHTING and WATCHMAN.

Lighting	Watchman	Mean Number of Burglaries
poor	no	2.80
good	no	1.00
poor	yes	2.40
good	yes	0.75

1. Using the Lenth procedure, find which effect(s) (if any) appear significant.

effects

2. Interpret all of these significant effects.
3. Permanently upgrading the lighting in the garage will cost $700 per month. Hiring awatchman will cost $3000 per month. It is estimated that lawsuits and loss of business cost on average $2000 per burglary. Is it worth it to hire a watchman, install lights or both?

Answer 1

a) The net mean burglaries of whole data is = (2.80+1.00+2.40+0.75)/4 = 1.7375

Since burglaries in scenario 1 and 3 are higher than the mean, hence they are significant

b) If lighting is poor, then the mean no of burglaries are significant as evident from previous answer. Having watchman doesnt influence much.

c) Cost of watchman = $3000

Cost of lighting = $700

Cost of burglary = $2000

Calculating the expected value of cost in each case

Note->

if watchman is included then $3000 cost is added else 0

If lighting is included then cost $700 is included else 0

Case 1) No lighting and no watchman

=> Expected value= 0X700 + 0X3000 + 2.80 X 2000 = $5600

Case 2) Good lighting and no watchman

=> Expected value= 1X700 + 0X3000 + 1X2000 = $2700

Case 3) No lighting and watchman

=> Expected value= 0X700 + 1X3000 + 2.40X2000 = $ 7800

Case 4) Lighting and watchman both

=> Expected value= 1X700 + 1X3000 + 0.75X2000 = $5200

Thus from above cases we can see that minimum cost is in case 2 ie $2700

Thus best decision is Lighting and no watchman.