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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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