Chi Square Test for Goodness of Fit. p. 846 1,5,8.
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Transcript of Chi Square Test for Goodness of Fit. p. 846 1,5,8.
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Chapter 14Day One
Chi Square Test for Goodness of Fit
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Homeworkp. 846 1,5,8
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Measure the distribution of a proportions within a single population.
Goodness of Fit: does specified population distribution seem valid
Homogeneity: compare two or more population proportions
CHI SQUARE TESTS
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M&Ms Advertised Color Distribtution
Brown Red Yellow Orange Blue Green
13 13 14 20 24 16
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Chi-Square Table
Brown
Red Yellow Orange
Blue Green Total
ObservedExpected(O-E)2/E
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Day Observed Count
Expected Count
(O-E)2/E
Sun 20Mon 133Tues 126Wed 159Thurs 136Fri 113Sat 12
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Example – Chi Square Test for Goodness of Fit Are you more likely to have a motor vehicle
collision when using a cell phone? A study of 699 drivers who were suing a cell phone when they were involved in a collision examined this question. The drivers made 26,798 cell phone calls during a 14-month period. Each of 699 collisions was classified in various ways. Here are the counts for each day of the week.
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Day Sun Mon Tues Wed Thurs Fri Sat TotalNumber 20 113 126 159 136 113 12 699
Ho: p Sun = pmon = pTues= ……Psat = 1/7
Ha: At least one of the proportions differs from the stated value
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Calculating p-values on Chi Squared Distribution.
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Example Chi Square Test for Homeogeneity of Populations Market researchers know that background music an influence
the mood and purchasing behavior of customers. One study in a supermarket in Northern Ireland compared three treatments: no music, French accordion music, and Italian string music. Under each condition, the researchers recorded the numbers of bottles of French, Italian, and other wine purchased. Here is a table that summarizes the data.
Populations: Population 1: bottles of wine sold while no music is playing Population 2: bottles of wine sold while French music is playing Population 3 : bottles of wine sold while Italian music is playing
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Ho: The proportions of each wine type sold are the same in all three populations
Ha: At least one proportion different
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Wine/music
None French Italian Total
French 30 39 30 99Italian 11 1 19 31Other 43 35 35 113Total 84 75 84 243
Observed Data
Expected Data
Wine/music
None French Italian Total
FrenchItalianOtherTotal
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