Final answer:
The 95% confidence interval for the true mean weight of textbooks, given a sample mean of 58 ounces, population standard deviation of 11.3 ounces, and sample size of 26, is approximately (53.659 ounces, 62.341 ounces).
Step-by-step explanation:
To construct a 95% confidence interval for the true mean weight of textbooks, when the sample mean is 58 ounces, population standard deviation is 11.3 ounces, and the sample size (n) is 26 textbooks, we start by finding the standard error of the mean and the z-score associated with a 95% confidence level.
The formula for standard error (SE) is:
SE = σ / √n
Where σ is the population standard deviation and n is the sample size.
SE = 11.3 ounces / √26 ≈ 2.215 ounces
For a 95% confidence level, the z-score is approximately 1.96. To find the confidence interval, we use the formula:
Mean ± (z-score * SE)
58 ounces ± (1.96 * 2.215 ounces) ≈ 58 ounces ± 4.341 ounces
Therefore, the 95% confidence interval is (58 - 4.341, 58 + 4.341) or approximately (53.659 ounces, 62.341 ounces).