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STAB22H3 (200)
Lecture

STAB22-C19.docx


Department
Statistics
Course Code
STAB22H3
Professor
Ken Butler

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CHAPTER 19 - CONFIDENCE INTERVALS FOR PROPORTIONS
MAIN TEXT
WHO - Sea fans
WHAT - % infected
WHEN - June 2000
WHERE - Las Redes Reef, Akumal, Mexico (40 ft deep)
WHY - Research
relevant info
-
n
= 104
- amt infected = 54/104
=>
= 51.9% = 0.519
- this is sample prop. for this particular random sample of sea fans that
were randomly collected from relevant loc.
- recall: sample prop's vary from one sample to another
CONFIDENCE INTERVAL
Known Information and Not Known
- we know:
- sample prop. retrieved from doing ONE SRS.
- we do not know:
p
- prop. of all infected sea fans on Las Redes Reef
- this is what we want to know

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- what else we know: sampling distribution of
is centred at
p
- SD of sampling distribution is given by:

Problem 2:
- do not know true standard deviation of sampling distribution model, b/c we do not
have
p

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- instead, we find standard error (SE()): estimated SD of sampling distribution of the
sample statistic (in this context, the prop.)
- standard error is estimated SD for sampling distribution
(ex)
- for sea fans, it is:

 
- sampling model for
- what they did was show the ±1SE, ±2SE, ±3SE, using retrieved sample prop.
NOTATION ALERT
-
- sample-based estimate of true prop
p
- q is 1 - p
- so q-hat = 1 -
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