Question

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 a larger confidence level. B. Use a smaller confidence level. C. 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. D. Use the same confidence level, but compute the interval n times. Approximately 5% of these intervals will be larger. E. None of the above. (b) A 95% confidence interval for the mean ? of a population is computed from a random sample and found to be 10±4. We may conclude A. that there is a 95% probability that ? is between 6 and 14. B. that there is a 95% probability that the true mean is 10 and a 95% chance the true margin of error is 4. C. 95% of the population is between 6 and 14. D. that if we took many, many additional samples and from each computed a 95% confidence interval for ?, approximately 95% of these intervals would contain ?. E. All of the above.

Answer 1

a)

a new confidence interval with larger width (larger margin of error) based on these same data can be obtained by

Use a larger confidence level.

b)

answer:

D. that if we took many, many additional samples and from each computed a 95% confidence interval for ?, approximately 95% of these intervals would contain ?.