Question

A sample of n-64 scores has a mean of M - 68. Assuming that the population mean is - 60, find the 2-score for this sample: If it was obtained from a population with d = 16 If it was obtained from a population with a = 32 Z If it was obtained from a population with o = 48

Answer 1

The z-score for a sample mean of 68 from a population with a mean of 60 and standard deviations of 16, 32, and 48 are 4, 2, and approximately 1.33, respectively.

Step-by-step explanation:

The student is asking how to calculate a z-score for a sample with various population standard deviations (σ). The z-score is given by the formula Z = (M - μ) / (σ/√n), where M is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. In this case, M = 68, μ = 60, n = 64, and three different standard deviations are given (σ = 16, σ = 32, and σ = 48).

For σ = 16: Z = (68 - 60) / (16/√64) = 8 / (16/8) = 8 / 2 = 4.
For σ = 32: Z = (68 - 60) / (32/√64) = 8 / (32/8) = 8 / 4 = 2.
For σ = 48: Z = (68 - 60) / (48/√64) = 8 / (48/8) = 8 / 6 = approximately 1.33.