Question

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

Answer 1

Answer:

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.

Answer 2

Answer:

For this case the confidence interval is given by (6-3=3 , 6+3=9)

And we can conclude that with 99% of confidence the true mean is between 3 and 9

And the best interpretation for this case is:

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

Because NEVER the confidence interval can be interpreted as a chance or a probability.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample  

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$   (1)

For this case the confidence interval is given by (6-3=3 , 6+3=9)

And we can conclude that with 99% of confidence the true mean is between 3 and 9

And the best interpretation for this case is:

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

Because NEVER the confidence interval can be interpreted as a chance or a probability.