Question

question 8 (1 point)
a 95% confidence interval for the mean $mu$ of a population is computed from a random sample and found to be $10pm4$. we may conclude
all choices
that if we took many, many additional samples and from each computed a 95% confidence interval for $mu$, approximately 95% of these intervals would contain $mu$.
that there is a 95% probability that the true mean is 10 and a 95% chance the true margin of error is 4.
that there is a 95% probability that $mu$ is between 6 and 14.

Explanation:

Step1: Recall confidence - interval concept

A 95% confidence interval means that if we take many samples and compute a 95% confidence interval for each sample, approximately 95% of these intervals will contain the true population mean $\mu$.

Step2: Analyze each option

• The statement "if we took many, many additional samples and from each computed a 95% confidence interval for $\mu$, approximately 95% of these intervals would contain $\mu$" is correct by the definition of a confidence - interval.
• The statement "there is a 95% probability that the true mean is 10 and a 95% chance the true margin of error is 4" is incorrect. The sample mean is 10 and the margin of error is 4 for this particular sample, but the true mean is a fixed (but unknown) value, not a random variable with a 95% probability of being 10.
• The statement "there is a 95% probability that $\mu$ is between 6 and 14" is incorrect in the frequentist interpretation. The true mean $\mu$ is a fixed value, and it either is or is not in the interval [6, 14]. The 95% refers to the long - run proportion of intervals that will contain $\mu$ when we take many samples.

Answer:

The correct choice is: that if we took many, many additional samples and from each computed a 95% confidence interval for $\mu$, approximately 95% of these intervals would contain $\mu$.