A chemical company wished to study the consistency of the strength of one of its liquid chemical products. The product is made in batches in large vats and then is barrelled. The barrels are subsequently stored for a period of time in a warehouse. To examine the consistency of the strength of the chemical, an analyst randomly selected five different batches of the product from the warehouse and then selected four barrels per batch at random. The strength of the chemical was determined on three samples per barrel. The data on strength follow:
Bitch 1 Bath 2 Batch 3
Barre 1234 123 4 1234
2.3 2.5 2.6 2.4 22 2.7 2.6 2.4 3.0 3.4 2.9 3.1
2.1 2.3 2.4 2.6 2.9 2.5 2.6 2.8 3.1 3.3 3.0 21
2.0 2.5 2.7 2.3 2.6 2.8 22 2.6 2.9 3.0 3.2 32
Batch 4 Batch 5
Bane 1 2 3 4 1 2 3 4
2.5 21 3.1 2.7 36 3.8 3.7 3.9
22 3.0 2.8 2.9 3.7 3.8 3.5 33
26 2.7 2.9 2.6 3.4 3.5 3.5 3.4
The main questions are:
- can the company rely on the fact that the strength of the chemical is identical from batch to batch and from barrel to barrel?
- what is the mean strength of the chemical in these stored barrels? How prccisc is that estimate?
- when a barrel is opened and part of it is sold, what can be told to the customer about the expected strength of the chemical he bought?
As the customer knows that there is some variation in the strength of the chemical, can you give a measure for its typical spread for the sample of chemical he bought?