A simple random sample of 30 items resulted in a sample mean of 15. The population standard deviation is σ = 8. Round your answers to two decimal places.
a. What is the standard error of the mean, σx?
b. At 95% confidence, what is the margin of error?
To find the standard error of the mean (σx), you need to divide the population standard deviation (σ) by the square root of the sample size (n).
a. Standard Error of the Mean (σx) = σ / √n
Given:
Population standard deviation (σ) = 8
Sample size (n) = 30
Substituting the given values into the formula:
Standard Error of the Mean (σx) = 8 / √30
Using a calculator, you can calculate the standard error of the mean:
Standard Error of the Mean (σx) ≈ 1.46 (rounded to two decimal places)
Therefore, the standard error of the mean is approximately 1.46.
To find the margin of error at 95% confidence, you need to multiply the z-score corresponding to a 95% confidence level by the standard error of the mean (σx).
b. Margin of Error = z * σx
At a 95% confidence level, the z-score corresponding to a two-tailed test is 1.96.
Margin of Error = 1.96 * 1.46
Using a calculator, you can calculate the margin of error:
Margin of Error ≈ 2.86 (rounded to two decimal places)
Therefore, at 95% confidence, the margin of error is approximately 2.86.