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

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24 Sep 2019

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~ Statistics Lecture #7 ~

Being Probabilistically Confident

09/19/19

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

interpretation.

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

with…

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