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STAT 100 Study Guide - Final Guide: Central Limit Theorem, Blood Pressure, Process State

9 pages50 viewsFall 2018

Department
Statistics
Course Code
STAT 100
Professor
All
Study Guide
Final

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Simon Fraser University
STAT 100
Chance and Data Analysis
Winter 2018
Final
Professor: Gamage Perera
Exam Guide
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Confidence Interval
Confidence$interval$
A!statistic!is!a!number!that!summarizes!something!about!a!sample.
A!parameter!is!a!number!that!summarizes!something!about!a!population.
The!sample!proportion!(denoted!pˆ),!0.17,!estimates!the!population!proportion
Sampling$distributions$
For!every!random!sample!taken!the!p^!value!will!be!slightly!different
The!sampling!distribution!of!pˆ!describes!the!pattern!of!those!many!sample
proportion!values.
We!know!that!when!the!sample!size!n!is!reasonably!large,!the!sampling
distribution!of!pˆ!is!approximately!normal.
The!sampling!distribution!of!pˆ!has!a!mean!of!p,!the!true!population!proportion.
The!sampling!distribution!of!pˆ!has!a!standard!deviation!of:
o
Using$the$68,$94,$99.7$rule$
Since!the!sampling!distribution!of!pˆ!is!approximately!normal,!the!empirical!rule
tells!us!about!95%!of!all!possible!samples!will!produce!a!value!of!pˆ!within!2
standard!deviations!of!the!true!p!(which!is!unknown).
So!in!about!95%!of!samples,!pˆ!will!be!between!p!−!2!×!(sd)!and!p!+!2!×!(sd).
Then!logically,!in!about!95%!of!samples,!the!true!p!will!be!within!2!standard
deviations!of!whatever!pˆ!we!got!from!that!sample.
In!other!words,!in!about!95%!of!samples,!the!unknown!p!will!be!between!pˆ!−
2×(sd)!and!pˆ!+!2!×!(sd)
The!population!proportion!p!does!not!change!from!sample!to!sample.
It!is!the!sample!proportion!pˆ!that!changes!across!different!samples
Using!the!confidence!interval!formula!you!must!have!the!standard!deviation
before!calculation!your!interval
o
n
pp )1(
n
pp
p)1(
2
×±
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Different$confidence$intervals$
To!change!the!level!of!confidence,!we!just!adjust!the!number!of!standard
deviations!in!the!“margin!of!error”!part!of!the!formula.
Actually!for!99%!confidence,!we!would!use!2.58!rather!than!2!or!3.
So!99%!confidence!is!better!than!95%!confidence,!right?
In!some!ways,!it!is:!We!have!better!odds!that!the!interval!we!get!will!contain!the
true!parameter!value.
But!the!interval!will!also!be!wider!–!less!informative
For!90%!confidence,!we!would!use!1.64!rather!than!2.
This!is!more!precise!(more!informative)!than!the!95%!interval,!but!there’s!more
of!a!chance!that!a!90%!interval!will!miss!the!true!parameter!value,!across
repeated!samples.
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