Question

16. A scientist wishes to estimate the average depth of a local river. She wishes to be 99 percent confident that the estimate is accurate within 2 feet. From a previous study, the standard deviation of the depths was measured at 4.33 feet. For this to make statistical sense and be valid, determine the minimum sample size.

a. 30

b. 31

c. 32

d. 33

Answer 1

Solution:
Given in the question
Confidence level = 99% or 0.99
Margin of error(E) = 2 feet
The standard deviation of the depths ()= 4.33
We need to determine the minimum sample size which can be calculated as
Sample size n = (Zalpha/2 * /E)^2
At confidence level 0.99, level of significance = 1 - 0.99 = 0.01,
alpha/2 = 0.01/2 = 0.005
So From Z table we found Zalpha/2 = 2.575
Sample size n = (2.575*4.33/2)^2 = 31.08 or rounding off to next whole number 32
So Minimum sample size required = 32
So its correct answer is C. i.e. 32