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?

2.

ohn believes he randomly selects his choice in Rock Paper Scissors.  

His friend challenges him to record what he chooses over the next 3 months.  

Rock	15
Paper	19
Scissors	21

Do a full hypothesis test to see if the data is truly balanced.  

Answer 1

1. (a) Pooled variance is used to combine together variances from different samples by taking their weighted average, to get the "overall" variance.

(b) 19.75

		Col 1	Col 2	Col 3
Row 1	Observed	18	24	8
	Expected	19.75	22.22	8.02
Row 2	Observed	14	12	5
	Expected	12.25	13.78	4.98

2. The hypothesis being tested is:

H0: The data is truly balanced

Ha: The data is not truly balanced

observed	expected	O - E	(O - E)² / E
15	18.333	-3.333	0.606
19	18.333	0.667	0.024
21	18.333	2.667	0.388
55	55.000	0.000	1.018
1.02	chi-square
2	df
.6010	p-value

Since the p-value (0.6010) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we can conclude that the data is truly balanced.