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Lecture 12

STAT 2230 Lecture Notes - Lecture 12: Statistical Hypothesis Testing, Nabisco, Null HypothesisPremium

2 pages24 viewsWinter 2017

Department
Statistics
Course Code
STAT 2230
Professor
Andrew Mc Adam
Lecture
12

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Day 12: Analysis [Feb 03]
- ///// late
- picked up on page 29
- how do we use this to make a statistical hypothesis test?
- either:
- the two population mean score is 14 and I just obtained a
particularly under-performing sample, OR
- I should not have been assuming that μ = 14 in the first place
- more negative T-scale
- small p-value
- p = 0.0034 for this problem
- which means there is very strong evidence against the null hypothesis
- very strong evidence against the claim that students are performing
at the correct level
- example: chocolate chips
- in 1998, Nabisco ran an advertising campaign in which they claimed that
each 18-ounce bag of Chips Ahoy cookies would contain at least 1000
chocolate chips
- test this claim
- population: all bags of cookies
- mean # of chips = μ
- standard deviation = sigma
- null hypothesis: H0: μ = 1000
- alternate hypothesis: HA: μ > 1000
- a group of consumers purchased a sample of bags of cookies and
counted the number of chocolate chips in each bag
- what sort of evidence would convince you that Nabisco were telling the
truth?
- I would be convinced by large sample means
- T = (ȳ - μ) / (s/sqrt(n))
- large positive T → small p
- in reality, the sample had n = 50 observations with a sample mean of ȳ =
1175 number of chocolate chips per bag, with a standard deviation of s =
292
-T = (ȳ - μ) / (s/sqrt(n)) → assume that the H0 is true, and use 1000
as μ
- T = (1175 - 1000) / (292 / sqrt(50))
- T = 4.20
- use R to calculate p
- p = 1 - pt(4.2, 49)
- p = 0.000056 → 0.0056%
- p > 0.01
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