Question

a.

Describe the Pooled variance assumption. How does it change the standard error? What impact does it have on a test statistic? What impact does it have on a p-value?

How do you justify making the assumption?

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b.

Republican	Democrat	Libertarian
Support	18	24	8
Don't Support	14	12	5

The above contingency table was created by asking a sample of people in a given area if they support a measure taken by the government.  

If The variables were independent how many Republicans in our sample would we expect to Support the measure proposed?

Answer 1

a. Pooled variance assumption: All the variables or groups has same variance.

Change in standard error: Decrease in the standard error due to pooling the variance as this pooled variance is more stable.

Change in test statistic: as the standard error decreases there will be an increase in the test statistic. By increasing the test statistic we'll be decreasing the p-value as there will be less extreme value left.

b. If the variables were independent then the expected number of Republicans in our sample who would be expected to Support the measure proposed is: