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Lecture_27,_Chap_12,_Sec_1

# Lecture_27,_Chap_12,_Sec_1 - Chapter 12 Section 1...

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Chapter 12 Section 1 Goodness-of-Fit Test

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Sullivan – Statistics : Informed Decisions Using Data – 2 nd Edition – Chapter 12 Section 1 – Slide 2 of 20 Goodness-of-Fit Test Learning objective Perform a goodness-of-fit test 1
Sullivan – Statistics : Informed Decisions Using Data – 2 nd Edition – Chapter 12 Section 1 – Slide 3 of 20 Goodness-of-Fit Test Instead of measuring a particular parameter (such as the mean), here we analyze whether a set of counts is as we expect We roll a die 600 times – does this set of counts differ significantly from the expected 100 per category? We are told that 40% of new cars that are sold are white, 45% are black, and 15% are red. If we take a random sample of 100 cars, does our actual count differ significantly from what we expected?

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Sullivan – Statistics : Informed Decisions Using Data – 2 nd Edition – Chapter 12 Section 1 – Slide 4 of 20 Goodness-of-Fit Test A goodness-of-fit test is a procedure used in inferential statistics that compares observed frequencies and expected frequencies For example, if we have the results of 600 rolls of a die 1 2 3 4 5 6 Actual Number 90 105 115 95 95 100 Expected Number 100 100 100 100 100 100 Is the die a fair one?
Sullivan – Statistics : Informed Decisions Using Data – 2 nd Edition – Chapter 12 Section 1 – Slide 5 of 20 Goodness-of-Fit Test Goodness-of-fit tests apply to experiments that consist of a series of n independent trials Each trial has k ≥ 3 different possible outcomes We let p 1 , p 2 , …, p k be the probabilities of the k outcomes (one p i for each of the possible outcomes)

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Sullivan – Statistics : Informed Decisions Using Data – 2 nd Edition – Chapter 12 Section 1 – Slide 6 of 20 Goodness-of-Fit Test Goodness-of-fit tests use the χ 2 distribution The χ 2 distribution has the following properties Its values are greater than or equal to zero It is not symmetric, it is skewed right Its shape depends on the degrees of freedom As the number of degrees of freedom increases, the shapes of the χ 2 distributions become more and more symmetric
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