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Unformatted text preview: = σX = σ/ n = 0.4/10 = 0.04. So the average of the GPA’s
¯
for a sample of 100 students is distributed with mean 3 and standard error 0.04.
With n = 100 being large enough, CLT theorem tells us the sample mean will be
approximately normally distributed, even if the GPAs are not normally distributed. So we
can calculate the probability
P ( X > 3 .1 ) = 1 − P ( X < 3 .1 )
3 .1 − 3
= 1 − P (Z <
) = 1 − P (Z < 2.5)
0.04 = 1 − 0.9938 = 0.0062 Exercise: Now assume that population distribution is also normal. Calculate P (X > 3.1).
Explain the source of the diﬀerence. Utku Suleymanoglu (UMich) Sampling Distributions 16 / 21 Sampling Distribution of P P as an Estimator of Sample Proportion
Say there is a binary characteristic: being left handed, being a woman, being from Sri
Lanka, being a American made car. . .
And you have a sample with subjects with many characteristics. Let’s focus male vs
female issue. You want to estimate the proportion of the female students for all college
students in the US. And you have a sample of 100 students 58 of which are female.
What is your best guess for the proportion...
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 Spring '08
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