The minimum sample size n required to estimate a population mean with 95% confidence and the desired margin of error 1.5 was found to be 198. Which of the following is the approximate value of the assumed estimate of the population standard deviation?
A) 10.7690
B) 12.8309
C) 115.9671
D) 164.6326

Question

Quizplus · Accepted Answer

We know that the formula for calculating the minimum sample size n is given by:

n = [(z-value)² * σ²] / E²

Where,
z-value = 1.96 (for 95% confidence level)
E = 1.5 (desired margin of error)

We can rearrange this formula to solve for σ (population standard deviation) as follows:

σ = sqrt[(n * E²) / (z-value)²]

Substituting the given values, we get:

σ = sqrt[(198 * 1.5²) / 1.96²] = 10.7690 (approx.)

Therefore, the assumed estimate of the population standard deviation is approximately 10.7690, which is closest to option A).

The Minimum Sample Size N Required to Estimate a Population