Question

A potato chip company produces a large number of potato chip bags each day and wants to investigate whether a new packaging machine will lower the proportion of bags that are damaged. The company selected a random sample of 150 bags from the old machine and found that 15 percent of the bags were damaged, then selected a random sample of 200 bags from the new machine and found that 8 percent were damaged. Let p^O represent the sample proportion of bags packaged on the old machine that are damaged, pˆN represent the sample proportion of bags packaged on the new machine that are damaged, pˆC represent the combined proportion of damaged bags from both machines, and nO and nN represent the respective sample sizes for the old machine and new machine.

Required:
Have the conditions for statistical inference for testing a difference in population proportions been met?

Answer 1

The conditions for the approximation have been met

Explanation:

Random samples on both cases and

p∧o proportion of bags packaged on the old machine that are damaged

p∧n sample proportion of bags packaged on the new machine that are damaged

p∧c = ( p∧o + p∧n ) / (nO + nN )

p∧o = 15 % p∧o = 0,15 nO = 150

p∧o * nO = 0,15 *150 p∧o * nO = 22,5

p∧n = 8 % p∧n = 0,08 nN = 200

p∧n*nN = 0,08 * 200 p∧n*nN = 16

Both p∧n*nN and p∧o * nO are bigger than 5

Therefore both samples are big enough for the approximation of the binomial distribution to normal distribution