Question

A sample of size n=60 is drawn from a population whose standard deviation is a=48. Find the margin of error for a 95% confidence interval for μ. Round the

answer to at least three decimal places.
The margin of error for a 95% confidence interval for u is

Answer 1

The formula for the margin of error (E) for a 95% confidence interval is:

E = 1.96 * (σ / sqrt(n))

where σ is the population standard deviation, n is the sample size, and 1.96 is the z-score corresponding to a 95% confidence level.

Substituting the given values, we get:

E = 1.96 * (48 / sqrt(60))

E ≈ 12.524 (rounded to three decimal places)

Therefore, the margin of error for a 95% confidence interval for the population mean (μ) is approximately 12.524. This means that we can be 95% confident that the true population mean falls within the interval (sample mean - 12.524, sample mean + 12.524).