A study of peach trees found that the average number of peaches per tree was 1025. The standard deviation of the population is 35 peaches per tree. A scientist wishes to find the
99% confidence interval for the mean number of peaches per tree. How many trees does
She need to sample to obtain an average accurate to within 18 peaches per tree?
A) 23
B) 26
C) 21
D) 4

Question

Quizplus · Accepted Answer

To find the sample size needed to estimate the population mean with a certain level of confidence and margin of error, we use the formula for the sample size of a mean: $n = \left(\frac{Z \cdot \sigma}{E}\right)^2$, where $Z$ is the Z-score corresponding to the confidence level, $\sigma$ is the population standard deviation, and $E$ is the margin of error. For a 99% confidence interval, the Z-score is approximately 2.576. Given $\sigma = 35$ peaches and $E = 18$ peaches, we calculate $n = \left(\frac{2.576 \cdot 35}{18}\right)^2$, which gives a value close to 26 when rounded to the nearest whole number. Therefore, the scientist needs to sample 26 trees.

A Study of Peach Trees Found That the Average Number