Question

Assume that a sample is used to estimate a population proportion p. Find the margin of error M.E. that corresponds to a sample of size 295 with 86 successes at a confidence level of 99.9%.

Answer 1

In Mathematics, particularly statistics, to find the margin of error for a sample size of 295 with 86 successes and a 99.9% confidence level, one must calculate the sample proportion, find the appropriate z-score, and apply the margin of error formula.

Step-by-step explanation:

The subject in question is estimating the margin of error for a population proportion, which is a key concept in statistics, a branch of Mathematics. Given a sample size of 295 with 86 successes, we want to find the margin of error (M.E.) for a 99.9% confidence level. The formula for the margin of error in this context (EBP) is ME = z * √(p' * (1 - p') / n), where z is the z-score corresponding to the confidence level, p' is the sample proportion, and n is the sample size.

First, calculate the sample proportion (p') by dividing the number of successes by the sample size: p' = 86/295. Then, find the z-score for the 99.9% confidence level, which is typically around 3.291 using a z-table. Finally, plug these values into the formula to calculate the margin of error.

Steps to calculate margin of error:

1. Compute the sample proportion (p') by dividing successes by total sample size (p' = 86/295).
2. Find the z-score for a 99.9% confidence level (approximately 3.291).
3. Insert values into the margin of error formula to obtain the EBP.