Question

It is known that the population variance (σ^2) is 125. At 95% confidence, what sample size should be taken so that the margin of error does not exceed 3?

a. 55
b. 53
c. 52
d. 54.

Answer 1

To determine the sample size needed for a 95% confidence level and a margin of error of 3, you can use the formula n = (Zα/2 * σ / E)^2, where n is the sample size, Zα/2 is the Z-score for the desired confidence level, σ is the population standard deviation, and E is the margin of error. Plugging in the values, the sample size needed is approximately 54.

Step-by-step explanation:

To determine the sample size needed, we can use the formula:

n = (Zα/2 * σ / E)2

Where:

• n is the sample size
• Zα/2 is the Z-score corresponding to the desired confidence level (95% confidence corresponds to Zα/2 = 1.96)
• σ is the population standard deviation (given as σ = √σ^2 = √125 = 11.18)
• E is the desired margin of error (given as E = 3)

Plugging in the values, we get:

n = (1.96 * 11.18 / 3)2 ≈ 54.02

Rounding up to the nearest whole number, the sample size needed is approximately 54.