It is claimed that by using an automatic filling machine, the average amount of chips in each bag is 100 grams

Question

It is claimed that by using an automatic filling machine, the average amount of chips in each bag is 100 grams. A random sample of 12 bags of chips showed a mean weight of 101.25 grams with a standard deviation of 2.5 grams. Is the machine operating properly at 0.05 level of significance?

Answer 1

For this sample, 100 lies at -(1.25/2.5)σ = -0.5σ, which is within ±2σ, so given your criteria, the machine is operating properly.
From a practical standpoint, however, if the bag is marked 100 grams the producer must reject any bag weighing less than 100 g. Given this sample, about 31% of the output of this machine is being rejected by QC scales down the line. To ensure a low number of rejections factories use 3σ rather than 2σ. Using this sample, the output needs to be adjusted upward by 2.5σ, or 6.25 g to achieve a 0.3% rejection rate. This represents a 6.25% loss in revenue. The production manager will likely have maintenance personnel working on this machine at every opportunity to reduce the σ, and will be looking into purchase of a better machine.

Edit:
Most scale companies will do a lmao if you suggest an accuracy better than 3σ = 0.065%, even though they advertise a repeatability of 0.01%. 0.065% of 100 g is 6.5 g 6.5/3 = 2.167 g, so the operation of this machine really can't be improved very much.

Answer 2

It has to be that accurate.
By using very precise electronic scales, the weight in each bag is kept to within a very small tolerance. If you think that a chip company makes some 10,000 bags every minute and one chip is 0.05 grams, they'd be giving away hundreds of bags every day just by adding one extra chip per bag.
It's a difference of thousands of dollars a month if a single filler is off by even 0.05 gms.

Answer 3

potato chips 2day this baby he ate an entire bag a potato chips (kin length) 4 breakfast and then i ate some potato chips from julies lunch so as u an see I truthfully have not had mushrooms immediately so potato chips is lots betta

Answer 4

that's a statistical problem.. and involves a bell curve, and some formula.. sorry I have forgotten that formula, but I would try to get it.