Which statistical model is appropriate? "Consider a factory producing sliced Ham...."
Hi all you knowledgeable people,
I am trying to get by grips around a problem that I can best explain by a example (below) - I am struggling to determine what statistical model I should assume in attacking the problem.
Consider a factory producing sliced Ham. The weight of all slices produced in a batch is known to be Gaussian distributed with a certain known, equal variance for each and all of the batches. The mean of the batches vary a little from batch to batch as slicing machines have to be taken apart, cleaned, assembled and adjusted between each batch.
When looking at all ham slices from all batches collectively the weight of a slice is also nicely Gaussian distributed with a certain mean, and with a variance that is obviously larger than that for the batches. I call this the long term statistical data.
Now, if we go to the factory on a random day and pick a random slice for weighing, our expectations to the weight of that slice would be governed by the long term statistical data – right?
The question is now: Given that we now have obtained a little bit of info about the specific batch (the weight of one sample from the particular batch), what would be our expectation to a second sample from that same batch? Given the fact that we know that the variance within a batch is much smaller that of the long term, would a single sample tell us if the cutter has been adjusted a little to one or the other side on that particular day? …and if so, what does it say?
Basically, What would be the mean and variance of the expectation-distribution for sample two?
And what about the expectations to a third sample from same batch after having obtained the weight of first two samples?
Which statistical theory should I be studying to work with my problem.
Hi all you knowledgeable people,
I am trying to get by grips around a problem that I can best explain by a example (below) - I am struggling to determine what statistical model I should assume in attacking the problem.
Consider a factory producing sliced Ham. The weight of all slices produced in a batch is known to be Gaussian distributed with a certain known, equal variance for each and all of the batches. The mean of the batches vary a little from batch to batch as slicing machines have to be taken apart, cleaned, assembled and adjusted between each batch.
When looking at all ham slices from all batches collectively the weight of a slice is also nicely Gaussian distributed with a certain mean, and with a variance that is obviously larger than that for the batches. I call this the long term statistical data.
Now, if we go to the factory on a random day and pick a random slice for weighing, our expectations to the weight of that slice would be governed by the long term statistical data – right?
The question is now: Given that we now have obtained a little bit of info about the specific batch (the weight of one sample from the particular batch), what would be our expectation to a second sample from that same batch? Given the fact that we know that the variance within a batch is much smaller that of the long term, would a single sample tell us if the cutter has been adjusted a little to one or the other side on that particular day? …and if so, what does it say?
Basically, What would be the mean and variance of the expectation-distribution for sample two?
And what about the expectations to a third sample from same batch after having obtained the weight of first two samples?
Which statistical theory should I be studying to work with my problem.