Question

For a population with a mean of 40 and a standard deviation of 8 find the z-score corresponding to each of the following samples.
X = 34 for a sample of n = 1 score:

M = 34 for a sample of n = 4

M = 34 for a sample of n = 16

Answer 1

Answer:

a) -0.75

b) -1.5

c) -3

Step-by-step explanation:

The question asks to convert a given value to z score with different sample sizes.

We are given:

Population Mean = u = 40

and

Standard deviation = s = 8

The task is to convert 34 to z-score using 3 different sample sizes.

For a given sample size "n", the formula to calculate the z-score is:

$z=\frac{x-u}{\frac{s}{\sqrt{n} } }$

For x = 34 and n=1, we get:

$z-score=\frac{34-40}{\frac{8}{\sqrt{1} } } = -0.75$

For x = 34 and n = 4, we get:

$z-score=\frac{34-40}{\frac{8}{\sqrt{4} } } = -1.5$

For x = 34 and n = 16, we get:

$z-score=\frac{34-40}{\frac{8}{\sqrt{16} } } = -3$

From here we can see that increasing the sample sizes increases the magnitude of z-score.