You measure 21 randomly selected textbooks' weights, and find they have a mean weight of 61 ounces. Assume the population standard deviation is 3.9 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, we use the formula:

Confidence interval = sample mean ± (critical value) * (standard deviation / sqrt(sample size))

First, to find the critical value, we need to look up the z-score associated with a 99% confidence level. The z-score for a 99% confidence level is 2.576.

Next, we substitute the given values into the formula:

Confidence interval = 61 ± (2.576) * (3.9 / sqrt(21))

To calculate the standard error (standard deviation / sqrt(sample size)):

Standard error = 3.9 / sqrt(21) ≈ 0.849

Finally, we substitute the values into the formula to find the confidence interval:

Confidence interval = 61 ± (2.576) * (0.849)

Confidence interval = 61 ± 2.186

Thus, the 99% confidence interval for the true population mean textbook weight is approximately (58.814, 63.186) ounces.