Central Middle School has calculated a 95 confidence interva

Central Middle School has calculated a 95% confidence interval for the mean height () of 11-year-old boys at their school and found it to be 56 ± 2 inches.

(a) Determine whether each of the following statements is true or false.

There is a 95% probability that is between 54 and 58.

There is a 95% probability that the true mean is 56, and there is a 95% chance that the true margin of error is 2.

If we took many additional random samples of the same size and from each computed a 95% confidence interval for , approximately 95% of these intervals would contain .

If we took many additional random samples of the same size and from each computed a 95% confidence interval for , approximately 95% of the time would fall between 54 and 58.

(b) Which of the following could be the 90% confidence interval based on the same data?

56±1

56±2

56±3

Without knowing the sample size, any of the above answers could be the 90% confidence interval.

Solution