[bushindo]

Here's problem from real life.

Suppose that at a certain company, valuable products are stolen over a 4-months periods, presumably by some employee. In the 114 days period, products were stolen in 45 different days. The company keeps a log file of the days the products were stolen. They then looked at the records to see who worked on what day. The following is the contingency table in terms of days for employee A

					 Onschedule			   Off-schedule

Stolen					 45							0						   

Non-Stolen				 32							37

The evidence looks pretty damning. But you need to convince a judge that it is more than chance. Assume that the chance of product being stolen is binomial and independent for each day with p = 45/114. That is, each day has a 45/114 chance of having product stolen. Calculate the likelihood that A's work days would have the same pattern as above, given the binomial loss assumption. Show your math.

Edited June 25, 2009 by bushindo

[bushindo]

Here's problem from real life.

Suppose that at a certain company, valuable products are stolen over a 4-months periods, presumably by some employee. In the 114 days period, products were stolen in 45 different days. The company keeps a log file of the days the products were stolen. They then looked at the records to see who worked on what day. The following is the contingency table in terms of days for employee A

					 Onschedule			   Off-schedule

Stolen					 45							0						   

Non-Stolen				 32							37

The evidence looks pretty damning. But you need to convince a judge that it is more than chance. Assume that the chance of product being stolen is binomial and independent for each day with p = 45/114. That is, each day has a 45/114 chance of having product stolen. Calculate the likelihood that A's work days would have the same pattern as above, given the binomial loss assumption. Show your math.

Here's part B of the question. What is the chance that we would get the above data if we assume

B) That the chance that a drug is stolen is the same for the on-schedule days as it is for the off-schedule days for employee A?

C) That the employee's on-off schedule days are independent of the stealing-activity days?