5.) Suppose I know that a 95% z-confidence interval for the ages of all US milli

Question

5.) Suppose I know that a 95% z-confidence interval for the ages of all US millionaires found their ages to be between 54.3 and 62.8 years old. This information came from a simple random sample of 100 millionaires.
a.) Which of the following statement(s) is/are true:

A: 95% of all US millionaires are between the ages of 54.3 and 62.8


B: There is a 95% chance that the mean age of all US millionaires is between
54.3 and 68.2


C: We can be 95% confident that the mean age of all US millionaires is between
54.3 and 62.8


D: The probability is 0.95 that the mean age of all US millionaires is between 54.3 and 62.8


E: The probability that we selected a sample whose 95% confidence interval
contains the population mean age is 0.95


b.) Based on this confidence interval, what is the sample mean and what is the margin of error?

Explanation / Answer

The meaning of this CI should be: I am 95% confident that the average age of these 100 millionaires is between 54.3 and 62.8.

So A) is not correct. I do not think B) is correct, since it uses Chance instead of Confident. C) is correct. I think D) is correct. E) is not correct.

Sample mean should between 54.3 and 62.8, if we have to calculate it, I will use (54.3+62.8)/2=58.55.

The margin of error is 0.05.

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