To estimate the mean number of pages per book in the fiction section of the large school library, we can use a t-test. A t-test is a statistical method for determining the probability that a given sample of data comes from a population with a certain mean value.
Given that the sample size is 35 and the standard deviation is 47.6 pages per book, we can use the t-distribution table to find the t-value for a 99% confidence level.
The t-value for a 99% confidence level and 34 degrees of freedom (sample size - 1) is 2.021.
With this information, we can construct a confidence interval for the mean number of pages per book in the fiction section of the large school library. The confidence interval is given by:
Sample mean ± t-value * (Standard deviation / √Sample size)
Therefore, the confidence interval for the mean number of pages per book in the fiction section of the large school library is:
291.8 ± 2.021 * (47.6 / √35)
The margin of error is approximately 12.2 pages per book.
So the mean number of pages per book in the fiction section of the large school library is between 279.6 and 304 pages per book with a 99% confidence level.