Researchers with the state Department of Natural Resources (DNR) wish to estimate the mean flow rate of water through a stream.From previous research conducted on similar streams, they know that the variance of flow rate is 27,556 gpm2.If the DNR researchers wish to create an interval that they are 99% confident will contain the mean flow rate with a bound on the error of estimation of 40 gpm, how many flow samples do they need?
A) 114
B) 3,148,739
C) 165
D) 115

Question

Quizplus · Accepted Answer

The formula for the margin of error is:
margin of error = z*(standard deviation/sqrt(sample size))
where z is the z-score for the desired level of confidence (2.576 for 99% confidence), standard deviation is the square root of the variance (sqrt(27,556) = 166.11 gpm), and sqrt(sample size) is the square root of the number of samples.

Solving the formula for the sample size, we get:
sample size = (z*standard deviation/margin of error)^2

Plugging in the values given in the problem, we get:
sample size = (2.576*166.11/40)^2 = 114.85

Therefore, the DNR researchers need at least 115 flow samples to estimate the mean flow rate with a 99% confidence interval that has a bound on the error of estimation of 40 gpm.

Researchers with the State Department of Natural Resources (DNR) Wish