Question

A sample of n=25 scores has a mean of m=68. find the z-score for this sample: a. if it was obtained from a population with =60 and =10.

Answer 1

The z-score is calculated using the formula Z = (sample mean - population mean) / (population standard deviation / sqrt(sample size)). For the given values, the z-score is 4.

Step-by-step explanation:

The student is asking how to calculate the z-score for a sample mean when the population mean and standard deviation are known. Given a sample mean (m) of 68, a population mean (μ) of 60, and a population standard deviation (σ) of 10, the z-score can be found using the formula:

Z = (m - μ) / (σ / √n)

With the values provided:

Z = (68 - 60) / (10 / √25)

Z = 8 / (10 / 5)

Z = 8 / 2

Z = 4

Thus, the z-score for this sample is 4.