AP Statistics Section 14.2 A

The two-sample z procedures of chapter 13 allowed us to compare the proportions of

successes in two groups (either two populations or two treatment groups in an experiment). We

need a new statistical test if we want to compare more than two groups.

A contingency table (or two-way frequency table) is a table in which frequencies correspond to two variables. One variable categorizes rows

and the other columns.

Discussed earlier in section 4.2.

Example 14.1: Market researchers know that background music can 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:

  Music  

  None French Italian Total

                            French 30 39 30 99 

Wine         Italian 11 1 19 31 

Chosen               Other 43 35 35 113 

                            Total 84 75 84 243

Section 14.2 presents two types of hypothesis testing based on contingency tables.

Tests of homogeneity are used to determine whether different populations have the same

proportion of some characteristic.

Tests of independence are used to determine whether a contingency table’s row variable is

independent of its column variable.

Both types of tests use the same basic methods from section 14.1. Test Statistic: where E = We find one primary test statistic by finding the sum of the test statistics for each cell in the tableThe degrees of freedom equal ___________________________ Conditions: Data must come from independent SRS’s of the populations of interest.All expected cell counts are greater than 1 and no more than 20% are less than 5

E

EO 22

totalgrand

al)column tot)( totalrow(

1)- columns of 1)(# - rows (#

Use a test to compare the distribution of wines selected for

each type of music.

2

Hypothesis: The populations of interest are _______________________ and

____________________

H0:__________________________________________

Ha:__________________________________________

sother wine andItalian French,

music no andItalian French,

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Conditions:

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9.57. being

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t.replacemen w/osampling since10n N assume alsoMust

t.independen are sales assume toreasonable Seems

Calculations:

28.1822.34

)22.3430( 22

28.18

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.001 value-P

Test2:C TESTS STATS

matrix ain dataInput :TI83/84

Conclusions:

sales. on wineeffect an has

played music of type that theconclude and H reject the weso

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