Question

A survey was conducted that asked 1002 people how many books they had read in the past year. Results indicated that x = 10.7 books and s = 16.6 books, construct a 99% confidence interval for the mean number of books people read. Interpret the interval

Answer 1

To construct a 99% confidence interval for the mean number of books people read, we can use the formula: x ± Z * (s / √n), where x is the sample mean, s is the sample standard deviation, Z is the z-score corresponding to the desired confidence level, and n is the sample size. In this case, x = 10.7, s = 16.6, n = 1002. The z-score for a 99% confidence level is approximately 2.576.

Step-by-step explanation:

To construct a 99% confidence interval for the mean number of books people read, we can use the formula:

x ± Z * (s / √n)

where x is the sample mean, s is the sample standard deviation, Z is the z-score corresponding to the desired confidence level, and n is the sample size. In this case, x = 10.7, s = 16.6, n = 1002. The z-score for a 99% confidence level is approximately 2.576. Plugging these values into the formula, we get:

10.7 ± 2.576 * (16.6 / √1002) = (9.58, 11.82)

This means that we are 99% confident that the true mean number of books people read in the past year falls within the interval of 9.58 to 11.82.