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 pˆOp^O represent the sample proportion of bags packaged on the old machine that are damaged, pˆNp^N represent the sample proportion of bags packaged on the new machine that are damaged, pˆCp^C represent the combined proportion of damaged bags from both machines, and nOnO and nNnN 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? No, the condition for independence has not been met, because random samples were not selected. A No, the condition for independence has not been met, because the sample sizes are too large when compared to the corresponding population sizes. B No, the condition that the distribution of pˆO−pˆNp^O−p^N is approximately normal has not been met, because nN(pˆC)nN(p^C) is not greater than or equal to 10. C No, the condition that the distribution of pˆO−pˆNp^O−p^N is approximately normal has not been met, because nO(1−pˆC)nO(1−p^C) is not greater than or equal to 10. D All conditions for making statistical inference have been met.
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 pˆOp^O represent the sample proportion of bags packaged on the old machine that are damaged, pˆNp^N represent the sample proportion of bags packaged on the new machine that are damaged, pˆCp^C represent the combined proportion of damaged bags from both machines, and nOnO and nNnN 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?
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No, the condition for independence has not been met, because random samples were not selected.
A -
No, the condition for independence has not been met, because the sample sizes are too large when compared to the corresponding population sizes.
B -
No, the condition that the distribution of pˆO−pˆNp^O−p^N is approximately normal has not been met, because nN(pˆC)nN(p^C) is not greater than or equal to 10.
C -
No, the condition that the distribution of pˆO−pˆNp^O−p^N is approximately normal has not been met, because nO(1−pˆC)nO(1−p^C) is not greater than or equal to 10.
D -
All conditions for making statistical inference have been met.
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