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 pˆO 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. Have the conditions for statistical inference for testing a difference in population proportions been met?

A No, the condition for independence has not been met, because random samples were not selected.
B No, the condition for independence has not been met, because the sample sizes are too large when compared to the corresponding population sizes.
C No, the condition that the distribution of pˆO−pˆN is approximately normal has not been met, because nN(pˆC) is not greater than or equal to 10.
D No, the condition that the distribution of pˆO−pˆN is approximately normal has not been met, because nO(1−pˆC) is not greater than or equal to 10.
E All conditions for making statistical inference have been met.

Answer 1

If the conditions for statistical inference for testing a difference in population proportions been met then we can say that -(E )All conditions for making statistical inference have been met.

Step-by-step explanation:

We can test the claim and the assumptions about the population proportion under the following conditions

• The method of random sampling should be adopted by the company so as to ensure that the observation conducted is independent and not biased
• The outcome data of the sampled unit must give rise to two outputs -On that is said to be successful and the other that is said to be a failure

Thus we can say that by studying the question we can say that the above mentioned condition have been met.Hence

If the conditions for statistical inference for testing a difference in population proportions been met then we can say that -(E )All conditions for making statistical inference have been met.