Question

The minimum sample size needed to estimate a population mean within 2 units with a 95% confidence when the population standard deviation equals 8 is:

A) 62
B) 9
C) 8
D) 61

Answer 1

The minimum sample size needed to estimate a population mean within 2 units with a 95% confidence when the population standard deviation equals 8 is 237.

Step-by-step explanation:

To calculate the minimum sample size needed to estimate a population mean within a certain margin of error, we can use the formula:

n = (Z * σ / E)^2

Where:

• n is the sample size
• Z is the z-score corresponding to the desired level of confidence (for a 95% confidence level, Z = 1.96)
• σ is the population standard deviation
• E is the margin of error (in this case, 2 units)

Plug in the given values:

n = (1.96 * 8 / 2)^2

n = 15.36^2

n ≈ 236.09

Since the sample size cannot be a decimal, round up to the nearest whole number:

n = 237

Therefore, the minimum sample size needed to estimate a population mean within 2 units with a 95% confidence when the population standard deviation equals 8 is 237.