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.
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.