Lecture 8 Part I.pdf

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Central limit theorem for the mean:
Using standard normal table
The sample mean is usually within 2 standard errors of
the population mean.
With a certain “% of Confidence” (% of all samples),

Confidence Interval for the mean
• Confidence intervals provide more information than point
• Confidence intervals for means are intervals constructed using a
procedure (presented in the next section) that will contain the

where Z comes from the “z (standard normal)…table”

Confidence z


population mean a specified proportion of the times, typically
either 95% or 99% of the times.

Area from -Z to +Z

• These intervals are called 95% or 99% confidence intervals.

- Z +Z

Central limit theorem for the mean:
So what?

horizontal axis of the normal distribution curve, should be within


Recall that

µ, the unknown population mean
(to be estimated),
is a parameter,

But in practice you know the sample mean, and want to
guess the population mean!


is a statistic.