W4- Chi Square Testing

15 .18 Sixty-four students in an introductory college economics class were asked how many credits they had earned in college , and how certain they were about their choice of major . Research question

At .01 , is the degree of certainty independent of credits earned Ho the degree of certainty is independent of credits earned

Ha the degree of certainty is dependent of credits earned ? 2 (i-j (E - O )2 /E

Eij (Ti x Tj /N

dF (R - 1 (C - 1

E11 (23 21 /64 7 .5469

E12 (23 19 /64 6 .8281

p E13 (23 24 /64 8 .625

E21 (22 21 /64 7 .2188

E22 (22 19 /64 6 .5313

E23 (22 24 /64 8 .25

E31 (19 23 /64 6 .8281

E32 (19 22 /64 6 .5313

E33 (19 24 /64 7 .125 (E11 - O11 )2 /E11 (7 .5469 - 12 / 7 .5469 2 .6276 (E12 - O12 )2 /E12 (6 .8281 - 8 / 6 .8281 0 .2011 (E13 - O13 )2 /E13 (8 .625 - 3 / 8 .625 3 .6685 (E21 - O21 )2 /E21 (7 .2188 - 8 / 7 .2188 0 .0845 (E22 - O22 )2 /E22 (6 .5313 - 4 / 6 .5313 0 .981 (E23 - O23 )2 /E23 (8 .25 - 10 / 8 .25 0 .3712 (E31 - O31 )2 /E31 (6 .8281- 1 / 6 .8281 4 .9746 (E32 - O32 )2 /E32 (6 .5313 - 7 / 6 .5313 0 .0336 (E33 - O33 )2 /E33 (7 .125 - 11 / 7 .125 2 .1075 ?2 (i-j (E - O )2 /E (E11 - O11 /E11 (E33 - O33 /E33 15 .0496

dF (3 - 1 (3-1 4

At 0 .01 level of significance with 4 degrees of freedom ?2 15 .0496 13 .2767 . Then we conclude from the chi square table that

21 .0261

Then we conclude from the chi square table that

9 .4877

Then we conclude from the chi square table that

0 .05

Cockpit noise level is dependent of flight phase

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yu ?d of cola ? Volunteers tasted Coca-Cola Classic , Pepsi , Diet Coke , and Diet Pepsi , with the results shown below Research question : At .05 , is the correctness of the prediction different for the two types of cola drinkers ? Could you identify your favorite brand in this kind of test ? Since it is a 2 2 table , try also a two-tailed two-sample z test for ?1 ?2 (see Chapter 10 ) and verify that z2 is the same as your chi-square statistic . Which test do you prefer ? Why (Data are from Consumer Reports 56 , no . 8 [August 1991] ,

br 519

Regular Cola Diet Cola Row Yes , got it right 7 7 14

No , got it wrong 12 20 32

Column Ho the correctness of the prediction different for the two types of cola drinkers...