A 99% confidence interval for the mean μ of a population is computed from a random sample and found to be 6 ± 3. We may conclude that:

A. there is a 99% probability that μ is between 3 and 9.

B. there is a 99% probability that the true mean is 6, and there is a 99% chance that the true margin of error is 3.

C. All of the above.

D. if we took many, many additional random samples, and from each computed a 99% confidence interval for μ, approximately 99% of these intervals would contain μ

Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen.

Option A is correct.

A. there is a 99% probability that μ is between 3 and 9.

Since, A 99% confidence interval for the mean μ of a population is computed from a random sample and found to be 6 ± 3.

Mean μ is lies between 6 - 3 and 6 + 3

So, mean lies between 3 and 9.

Therefore, 99%  probability that μ is between 3 and 9.

Thus, option A is correct.

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A. there is a 99% probability that μ is between 3 and 9.

Step-by-step explanation:

From a random sample, we build a confidence interval, with a confidence level of x%.

The interpretation is that we are x% sure that the interval contains the true mean of the population.

In this problem:

99% confidence interval.

6 ± 3.

So between 6-3 = 3 and 6 + 3 = 9.

So we are 99% sure that the true population mean is between 3 and 9.

So the correct answer is:

A. there is a 99% probability that μ is between 3 and 9.

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