Question

a random sample of n = 49 scores is obtained from a population with σ = 14. if the sample mean is 4.50 points greater than the population mean, what is the z-score for the sample mean?

Answer 1

The z-score for the sample mean is 1.0714.

Step-by-step explanation:

To find the z-score for the sample mean, we can use the formula:

z = (X - μ) / (σ / √n)

where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, the sample mean is 4.50 points greater than the population mean, so X - μ = 4.50. The population standard deviation is given as σ = 14. The sample size is n = 49.

Substituting these values into the formula, we get:

z = (4.50) / (14 / √49)

Simplifying, z = 1.0714.