STA 210 Lecture Notes - Lecture 7: Confidence Interval, Sampling Distribution, Statistical Inference

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24 Sep 2019
~ Statistics Lecture #7 ~
Being Probabilistically Confident
o Big picture was missed by several with respect to what an SRS is and why it is critical.
o Lots Encountered in the Reading BN 2.13
o Sampling Error
What it is
Why we care
o Sampling Distribution
What is it
What we know, if our sampling was SRS-like
o Material Simplified as Much as Possible
o Margin of Error and Confidence Interval
95% and other how to compute
95% and other how to interpret
Essential probabilistic origins
o Less Confidence = Tighter Interval
o More Confidence = Wider Interval
o Interpretation: About _____ % of all survey samples of size (n) would produce a _____% confidence
interval that would contain the true percentage of (PARAMETER).
o What enables us to have a confidence interval formula?
o The probability that starts with the sampling
o The bridge to these simple MOE and confidence interval formulae is made possible by the
mathematics inherited from this probability.
No bridge, no formulas.
o The confidence provided by these tools is a probability-based confidence.
No way around that. Challenges the person-on-the-street to manage the
o Key Language from Reading
o Sampling variability
o Sampling distribution
You absolutely have to be very comfortable with these simple-sounding phrases.
o Sampling Variability
o The variability seen in a statistic from sample to sample is called sampling variability.”
How can you estimate the parameter in the face of this variability?
o Sampling variability is real. If you understand nothing else about our group activity, this is
one thing you have to know.
o Elementary statistical inference gives us all a way of getting a handle on this.
But to appreciate the handle, we have to appreciate the need.
o What is needed to produce a margin of error?
o Knowing that with SRS-type samples, sampling variability is predictable.
o Understanding that with other-type samples it is not.
o Recognizing that if sample is not a probabilistic sample, then it will be very difficult-to-
impossible to understand what the MOE is and how to form a confidence interval.
o Predictable? How?
o If you were to do the sampling over and over and plot the different statistics, you end up
o Then that plot- called a sampling distribution- would exhibit predictable characteristics.
o Your Sampling Distribution
o Will be bell shaped
o Will peak above the parameter
o Will be spread out in a way that is predictable if one only knows the way the sample was
taken, and the sample size
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