Question

You measure 35 textbooks' weights, and find they have a mean weight of 51 ounces. Assume the population standard deviation is 10.6 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook weight. Give your answers as decimals, to two places

Answer 1

To construct a 95% confidence interval for the true population mean textbook weight, use the formula CI = X ± Z * σ / √n. Based on the given information, the 95% confidence interval is (47.68, 54.32) ounces.

Step-by-step explanation:

To construct a 95% confidence interval for the true population mean textbook weight, we can use the formula: CI = X ± Z * σ / √n.

Where:
- CI is the confidence interval
- X is the sample mean (51 ounces)
- Z is the z-score corresponding to a 95% confidence level (1.96 for a two-tailed test)
- σ is the population standard deviation (10.6 ounces)
- n is the sample size (35 textbooks)

Using the formula: CI = 51 ± 1.96 * 10.6 / √35, we can calculate the confidence interval.

CI = 51 ± 3.32

So, the 95% confidence interval for the true population mean textbook weight is (47.68, 54.32) ounces.