Question 1: In a recent years the U.S. Mint in Denver manufactured 270 million q

Question

Question 1:

In a recent years the U.S. Mint in Denver manufactured 270 million quarters. As part of the mint's quality control program, samples of quarters are randomly selected each day for detailed inspection to confirm that they meet all required specification.

(a) Do you think the quarters are randomly selected with replacement or without replacement?

(b) Give reasons why statistical methods tends to be based on the assumption that sampling is conducted with replacement, instead of without replacement.

Explanation / Answer

(a) Quarters are randomly selected with replacement.

(b) This is because when I sample a with replacement then sample values are independant of each other, but if I sample without replacement, then my present sampling value is forced to take into consideration the previous sampled values i.e the present sample value is dependant on the value sampled before it. Please remember this effect happens when population are not very high. In cases of very high population with or without replace dont have much difference.

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