A Lab Manager is trying to find the number of defected items produced in two different shifts: Day and Night Shifts.
Day Shift = 20 items defected out of 2000 items.
Night Shift = 15 items defected out of 1300 items.
Let the defectiveness of the item follow poisson distribution.

If i am given a random sample group of 10 items(All are only from either Night of Day Shift) and 2 are defected out of them, find the most likely hood ratio and also find both Type 1 and Type 2 errors

Question

A Lab Manager is trying to find the number of defected items produced in two different shifts: Day and Night Shifts. 
Day Shift = 20 items defected out of 2000 items. 
Night Shift = 15 items defected out of 1300 items. 
Let the defectiveness of the item follow poisson distribution.

If i am given a random sample group of 10 items(All are only from either Night of Day Shift) and 2 are defected out of them, find the most likely hood ratio and also find both Type 1 and Type 2 errors

anonymous · Answer

please please help me

amistre64 · Answer

sorry, im not competent in the Poisson stuff.  My elementary stats class didnt even mention it.

anonymous · Answer

:( Thanks.

dumbcow · Answer

hmm well to evaluate lambda you need to take each shift and scale it to 10 items
2000/200 = 10   so  20/200 = 1/10
for every 10 items on avg 1/10 are defective

1300/130 = 10   so 15/130 = 3/26
for every 10 items on avg 3/26 are defective

these will be the respective lambdas
then you test for probability of random sample being from either Day shift or Night shift

dumbcow · Answer

$$P(X=2) = \frac{\lambda ^{2}e^{-\lambda}}{2!}$$

anonymous · Answer

So is that how i find the most likely hood ratio. ... ?... How do i find the Both Type1 and Type 2 Errorrs?