Question 885374: The value of a z score in a hypothesis test is influenced by a variety of factors. Assuming that all other variables are held constant, explain how the value of z is influenced by each of the following. Be sure to explainwhy this change would happen.a. Increasing the difference between the sample mean and the population mean.b. Increasing the population standard deviation.c. Increasing the sample siz
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the formula for z score is (x-m) / se
x is the sample mean
m is the population mean
se is the standard error which is equal to psd / sqrt(ss)
psd = population standard deviation
ss = sample size.
if you replace se with psd / sqrt(ss) in the formula of z = (x-m) / se, then you get:
z = (x-m) / (psd / sqrt(ss)) which can be simplified to:
z = ((x-m) * (sqrt(ss)) / psd.
if you increase the difference between x and m then the z score becomes larger because (x-m) is in the numerator of the simplified equation.
if you increase psd, then the z score becomes smaller because psd is in the denominator of the simplified equation.
if you increase the sample size, then the z score becomes larger because sqrt(ss) is in the numerator of the simplified equation.
example:
assume x = 100 and m = 80 and ss = 100 and psd = 10
formula for z score is (x-m) / se
se = psd / sqrt(ss) = 10 / sqrt(100) = 10 / 10 = 1
you have:
x = 100
m = 80
se = 1
z = (x-m) / se becomes z = (100 - 80) / 1 = 20 / 1 = 20
now increase the spread by making x = 120
you get:
z = (x-m) / se becomes z = (120 - 80) / 1 = 40 / 1 = 40
z got bigger.
now go back to the original values of:
x = 100
m = 80
psd = 10
ss = 100
increase psd from 10 to 20.
you get se = psd / sqrt(ss) = 20 / 10 = 2
you now have:
x = 100
m = 80
se = 2
z = (x-m) / se = 20/2 = 10
z got smaller because you increased the population standard deviation.
now go back to the original values of:
x = 100
m = 80
psd = 10
ss = 100
increase the sample size from 100 to 400.
you get se = psd / sqrt(ss) = 10 / 20 = .5
you now have:
x = 100
m - 80
se = .5
z = (x-m) / se = 20/.5 = 40
z got bigger because you increased the sample size from 100 to 400.
when you increase (x-m), z gets bigger.
when you increase psd, se gets bigger which makes z get smaller.
when you increase sample size, se gets smaller which makes z get bigger.
i have to run so don't have time to edit what i just wrote.
if you understand, then you're good.
if there's anything in here that confused you then send me an email and i'll provide a correction and or a better explanation.
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