z-score - Math Central

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Question from Sophia, a parent:

Indicate whether the factor influences the numerator or denominator of the z-score and determine whether the effect would be to increase the value of z(farther from zero) or decrease the value of z(closer to zero).
a. increase the sample size
b. increase the population standard deviation
c. increase the difference between the sample mean and the value of µ specified in the null hypothesis

Hi Sophia,
Look at the formula for z-score:

z transformation

x is the score to be tested, μ is the sample mean and σ is the standard deviation. If you consider it to be a fraction, think:

What happens to the value if you have a larger denominator? Is 1/2 or 1/4 bigger?
What happens to the value if you have a larger numerator? Is 3/4 or 1/4 bigger?

Hope this helps,

Janice

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