Question

You want to be 95% confident that the sample variance is within 40% of the population variance. find the appropriate minimum sample size. group of answer choices 11 57 224 14 previous next

Answer 1

To find the appropriate minimum sample size, you can use the formula n = (z^2 * σ^2) / E^2, where n is the sample size, z is the z-score corresponding to the desired confidence level, σ^2 is the population variance, and E is the acceptable percentage error. In this case, you want to be 95% confident that the sample variance is within 40% of the population variance.

Step-by-step explanation:

To find the appropriate minimum sample size, we can use the formula:

n = (z^2 * σ^2) / E^2

where:

n is the sample size,

z is the z-score corresponding to the desired confidence level,

σ^2 is the population variance, and

E is the acceptable percentage error.

In this case, we want to be 95% confident that the sample variance is within 40% of the population variance. Since the variance is a squared value, we need to use the squared acceptable percentage error, which is 0.4^2 = 0.16. The z-score for a 95% confidence level is approximately 1.96. Substituting these values into the formula, we get:

n = (1.96^2 * σ^2) / 0.16

Since we don't have the value of the population variance (σ^2), we cannot calculate the exact minimum sample size.