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Chi square test and independence of two variables

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In testing the independence of two variables described in a contingency table, determine the critical value of chi-square if the test is to be conducted at the
a. x = 0.025 level and df = 5
b. x = 0.05 level and df = 8
c. x = 0.01 level and df = 6
d. x = 0.10 level and df = 4

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Solution Summary

The solution provides step by step method for the calculation of a chi square statistic. The formula for the calculation and interpretations of the results are also included.

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Chi-square test for independence of variables and goodness of fit:
1) independence of variables: association between gender and seat belt usage
2) goodness of fit: does it appear that the sexes are equally probable

5) Chi-square test for independence of variables and goodness of fit
a) 1024 car drivers were classified according to gender and use of seat belts. The results are tabulated below:

SEAT BELT USAGE
DON'T USE USE
MALE 192 272
FEMALE 284 276

Does the data suggest an association between gender and seat belt usage?

b) A researcher wishes to determine if a particular breed of pig is equally likely to produce a male of female piglet. 106 litters of pig of this breed, each containing 8 piglets, were classified according to the number of male piglets in the litters. The results are tabulated below:

NUMBER OF MALE PIGLETS 0 1 2 3 4 5 6 7 8
FREQUENCY 0 5 9 22 25 26 14 4 1

From this data, does it appear that the sexes are equally probable?

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