Answer :
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:
[tex]z=\frac{x-u}{\frac{s}{\sqrt{n} } }[/tex]
For x = 34 and n=1, we get:
[tex]z-score=\frac{34-40}{\frac{8}{\sqrt{1} } } = -0.75[/tex]
For x = 34 and n = 4, we get:
[tex]z-score=\frac{34-40}{\frac{8}{\sqrt{4} } } = -1.5[/tex]
For x = 34 and n = 16, we get:
[tex]z-score=\frac{34-40}{\frac{8}{\sqrt{16} } } = -3[/tex]
From here we can see that increasing the sample sizes increases the magnitude of z-score.