Question

11. 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 u = 60 and o = 10. b. If it was obtained from a population with p = 60 and o = 20. c. If it was obtained from a population with u = 60 and o = 40.

Answer 1

(11) The formula to calculate the standardized score or z-score is

M -u N

where, sample mean, sample size, $\mu:$ population mean, $\sigma:$ population standard deviation

Given:

n = 25, M = 68

(a) When $\mathrm{\mu=60\:,\:\sigma=10}$

Μ - μ 68 α

So, the z-score is calculated as $\mathbf{{\color{Blue}z=4}}$

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(b) When

u= 60, 0 = 20

$\mathrm{z=\frac{M-\mu}{\frac{\sigma}{\sqrt{n}}}}=\mathrm{\frac{68-60}{\frac{20}{\sqrt{25}}}=\frac{8}{\frac{20}{5}}=\frac{8}{4}=\mathbf{2}}$

So, the z-score is calculated as $\mathbf{{\color{Blue}z=2}}$

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(c) When

u= 60, 0 = 40

Μ - μ 68 η | Ν

So, the z-score is calculated as $\mathbf{{\color{Blue} z=1}}$