A 95% confidence interval for the mean of a population is computed from a random

Question

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

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.

(b) 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. 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 smaller confidence level.

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.

Explanation / Answer

a)

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

by definition

b)

A. Use a larger confidence level. is correct

as confidence level increases , critical value increases and hence margin of error increase

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