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.

Question 2:

Height of adult females are normally distributed. Samples of heights of adult females, each of size n = 3, are randomly collected and the sample means are found. Is it correct to conclude that the sample means cannot be treated as a normal distribution because the sample size is too small? Explain.

Explanation / Answer

Question 2:

Here it is given that population is normally distributed. So sampling distribution of sample mean will be normal distribution regardless of sample size. That is it is not correct to conclude that the sample means cannot be treated as a normal distribution because the sample size is too small.

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