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Unformatted text preview: this chapter, we will assume the knowledge of µ and σ 2 of the population and ﬁgure
out the distribution of x .
Statistics is about estimation population parameters, so usually we don’t know µ or σ 2 .
We are mostly building up our arsenal for the next chapters.
Here is an example where it is plausible to know the population parameters:
Suppose we have a random sample of 100 Michigan students and we observe their
GPA’s. It is known that in the population (university) average GPA is 3 and standard
deviation of GPA is 0.4.
What is the probability of a randomly picked student having a GPA above 3.1 Can you
ﬁgure this out? NO, without further info about the population distribution of GPA’s. I
did not tell you what distribution population has. Utku Suleymanoglu (UMich) Sampling Distributions 15 / 21 Sampling Distributions But you can ﬁgure out the probability of the sample mean of 100 students’ GPA’s
exceeding 3.1! What is the sampling mean and the variance of x ?
E (X ) = µ = 3, V (X )...
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- Spring '08