A study of peach trees found that the average number of peaches per tree was 525. The standard deviation of the population is 105 peaches per tree. A scientist wishes to find the 80% 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 12 peaches per tree?
A) 77
B) 55
C) 83
D) 126

Question

Quizplus · Accepted Answer

To find the sample size needed for a certain level of accuracy, we can use the formula:

n = (z*σ / E)^2

where z is the z-score corresponding to the desired confidence level (80% = 1.28), σ is the population standard deviation, and E is the maximum desired margin of error (12 in this case).

Substituting the given values, we get:

n = (1.28*105 / 12)^2 = 126.06

Rounding up to the nearest whole number, we get n = 127.

Therefore, the scientist needs to sample 127 peach trees to obtain an average accurate to within 12 peaches per tree.

The closest answer choice to 127 is D (126), which is the best choice.

A Study of Peach Trees Found That the Average Number