For each problem, select the best response.

(a) Suppose you collect a SRS of size n from a population and from the data collected you computed a 95% confidence interval for the mean of the population. Which of the following would produce a new confidence interval with larger width (larger margin of error) based on these same data?

A. Use the same confidence level, but compute the interval n times. Approximately 5% of these intervals will be larger.
B. Nothing can guarantee absolutely that you will get a larger interval. One can only say the chance of obtaining a larger interval is 0.05.
C. Use a larger confidence level.
D. Use a smaller confidence level.
E. None of the above.

(b) A 95% confidence interval for the mean $\mu$ of a population is computed from a random sample and found to be $10 \pm 4$. We may conclude

A. that there is a 95% probability that $\mu$ is between 6 and 14.
B. 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 $\mu$.
C. 95% of the population is between 6 and 14.
D. that there is a 95% probability that the true mean is 10 and a 95% chance the true margin of error is 4.
E. All of the above.