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.

Construct a 99% confidence interval for the mean number of books people read and interpret the result. Select the correct choice below and fill in the answer boxes to complete your choice. (Use ascending order. Round to two decimal places as needed.)
A. There is a 99% chance that the true mean number of books read is between__and__
B. If repeated samples are taken, 99% of them will have a sample mean between__and__
C. There is 99% confidence that the population mean number of books read is between__and__

Answer 1

To construct a 99% confidence interval for the mean number of books people read, use the formula: CI = x ± z*(s/√n), where x is the sample mean, s is the sample standard deviation, n is the sample size, and z is the z-score corresponding to the desired confidence level. The 99% confidence interval for the mean number of books people read is approximately (9.02, 12.38).

Step-by-step explanation:

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

CI = x ± z*(s/√n)

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

CI = 10.7 ± 2.576*(16.6/√1002) ≈ 10.7 ± 1.685

Therefore, the 99% confidence interval for the mean number of books people read is approximately (9.02, 12.38).

Interpreting the interval, we can say with 99% confidence that the true mean number of books people read falls within this range. This means that if we were to conduct multiple surveys and calculate confidence intervals using the same method, we would expect 99 out of 100 intervals to contain the true population mean. The interval gives us an estimate of the likely range within which the true mean lies.