Question

1. a sample of ( n = 64 ) scores has a mean of ( m = 68 ). assuming that the population mean is ( mu = 60 ), find the z - score for this sample: a. if it was obtained from a population with ( sigma = 16 )

Explanation:

Step1: Recall the formula for the z - score of a sample mean

The formula for the z - score of a sample mean is \(z=\frac{M - \mu}{\frac{\sigma}{\sqrt{n}}}\), where \(M\) is the sample mean, \(\mu\) is the population mean, \(\sigma\) is the population standard deviation, and \(n\) is the sample size.

Step2: Substitute the given values into the formula for part (a)

Given \(M = 68\), \(\mu=60\), \(\sigma = 16\), and \(n = 64\). First, calculate \(\frac{\sigma}{\sqrt{n}}=\frac{16}{\sqrt{64}}=\frac{16}{8}=2\). Then, \(z=\frac{68 - 60}{2}=\frac{8}{2}=4\)

Answer:

The z - score for part (a) is \(4\)