What is the minimum sample size required to estimate a population mean with 95% confidence when the desired margin of error is D = 1.5? The population standard deviation is known to be 10.75.
A)n = 138
B)n = 139
C)n = 197
D)n = 198

Question

Quizplus · Accepted Answer

The formula for calculating the minimum sample size required to estimate a population mean with a margin of error is:

n = (z^2 * σ^2) / D^2

Where z is the z-score for the desired level of confidence, σ is the population standard deviation, and D is the desired margin of error.

For a 95% confidence level, the z-score is 1.96. Plugging in the given values, we get:

n = (1.96^2 * 10.75^2) / 1.5^2 = 198.35

Rounding up to the nearest whole number, the minimum sample size required is 198. Therefore, the correct answer is D.

What Is the Minimum Sample Size Required to Estimate a Population