What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is D = 1.25? The standard deviation in a preselected sample is 8.5.
A) n = 76
B) n = 125
C) n = 126
D) n = 190

Question

Quizplus · Accepted Answer

We know that,
Margin of error = z * (standard deviation / sqrt(n))
We have, 
Margin of error = 1.25
z (for 90% CI) = 1.645 (from standard normal distribution table)
standard deviation = 8.5
Let's plug in these values and solve for n,
1.25 = 1.645 * (8.5 / sqrt(n))
sqrt(n) = (1.645 * 8.5) / 1.25
sqrt(n) = 11.13
n = (11.13)^2
n = 123.944

Since sample size has to be a whole number, we round up to the nearest whole number to ensure that the margin of error is less than or equal to 1.25. Therefore, the minimum sample size required is n = 126.

What Is the Minimum Sample Size Required to Estimate a Population