Question

A simple random sample of 40 items resulted in a sample mean of 20 . The population standard deviation is σ=4. Round your answers to two decimal places. a. What is the standard error of the mean, σxˉ​ ? b. At 95% confidence, what is the margin of error?

Answer 1

a. The standard error of the mean is 0.632. b. The margin of error at 95% confidence is 1.24032. This margin of error provides a measure of uncertainty associated with the sample mean estimation in statistical analysis.

Step-by-step explanation:

a. The standard error of the mean (σxˉ) is determined by the formula σxˉ = σ/√n, where σ represents the population standard deviation, and n is the sample size.

In this context, with a known population standard deviation (σ) of 4 and a sample size (n) of 40, the standard error is calculated as σxˉ = 4/√40, yielding a result of 0.632.

b. When establishing a 95% confidence interval, the margin of error is derived from the formula margin of error = critical value * standard error.

With a critical value of 1.96 for a 95% confidence level, and the previously computed standard error (σxˉ) of 0.632, the margin of error is determined as 1.96 * 0.632, resulting in a margin of error of 1.24032.

This margin of error provides a measure of uncertainty associated with the sample mean estimation in statistical analysis.

Hence, the standard error of the mean is 0.632 and the margin of error at 95% confidence is 1.24032.