Question

INFERENCE FOR CATEGORICAL DATA DATA ACTIVITY 1) The table below organizes data on gender and responses to the following question: How intelligent do you think you are compared with others your age? Intelligence Count Female Below Average 437 Average 2243 Above Average 4072 Gender Male 456 1643 4593 1a) We would like to test whether there is a statistical difference between how males and females rate their intelligence compared to their peers. In this context, which is the explanatory variable and which is the response variable? Explain. 1b) State an appropriate null hypothesis and alternative hypothesis. 1c) Make a copy of the table. Calculate the row totals and column totals and enter them into your table. Then calculate the expected counts for each cell and enter the expected counts into ypur table. 1d) Calculate the chi-square test statistic. What are the degrees of freedom associated with the chi-square test statistic? 1e) Calculate the p-value and state your conclusion

Answer 1

1a) Our explanatory variable is gender and the response variable is intelligence. This is because we are checking the level of intelligence wrt gender and not gender wrt intelligence

1b) H0: Both Males and Females have similar level of intelligence or in other words, intelligence is not dependent on gender.

Ha: Intelligence is dependent on gender.

Observed Below Average Average Female 437 2243 Male 456 1643 Total 893 3886 Above Average Total 4072 6752 4593 6692 8665 13444 Expected Below Average Average Above Average Total Female 448.4927 1951.6715 4351.8358 6752 Male 444.5073 1934.3285 4313.1642 6692 Total 893 3886 8665 13444 (O-E)^2/E Below Average Average Above Average Total Female 0.2945 43.4870 17.9943 61.7757 Male 0.2971 43.8769 18.1556 62.3296 Total 0.5916 87.3638 36.1499 124.1053

For example -> Expected (Average, Male)=6692*3886/13444=1934.33 and similarly others.

dof=(2-1)*(3-1)=2dof

Chisq Stat=124.10

pvalue=Chisq(124.1,2)=0.000

As pvalue<0.01, we reject H0 and conclude there is enough evidence that the intelligence is dependent on gender.