Question

You measure 22 randomly selected textbooks' weights, and find they have a mean weight of 48 ounces. Assume the population standard deviation is 14.8 ounces. Based on this, construct a 99% confidence interval for the true population mean textbook weight.

Answer 1

To construct a 99% confidence interval for the true population mean textbook weight, use the formula: CI = X ± Z * σ/√n. Plugging in the given values, the confidence interval is approximately 40.108 to 55.892 ounces.

Step-by-step explanation:

To construct a 99% confidence interval for the true population mean textbook weight, we can use the formula:

CI = X ± Z * σ/√n

Where X is the sample mean (48 ounces), Z is the z-score corresponding to the desired confidence level (99% confidence corresponds to a z-score of approximately 2.576), σ is the population standard deviation (14.8 ounces), and n is the sample size (22).

Plugging in the values:

CI = 48 ± 2.576 * 14.8/√22

Calculating the confidence interval, we get:

CI ≈ 48 ± 7.892

Therefore, the 99% confidence interval for the true population mean textbook weight is approximately 40.108 to 55.892 ounces.