Question

Determine a hypothesis that the following data may address and perform a Chi-square test Goodness of Fit test on following data. (Outline H0 and H1, do the calculation--outline all your steps--and interpret the results, that is, link it back to either H0 or H1)

What is your political affiliation?

republican	102
democrat	98
total	200

Answer 1

Chi-Square Test

Null Hypothesis: Ho : There is no difference in the preference between republican versus democrat affiliation

Alternate hypothesis; Ha: There is significant difference in the preference between republican versus democrat affiliation

If the χ² (calculated) < χ² (table value) accept the null hypothesis at the 5% significant level otherwise reject the Ho and accept Ha.

Types of affiliation	Actual affiliation (O)	Expected Affiliation (E)	(O – E)2	(O – E)2/E
Republic	102	200/2 = 100	(102 – 100)2 = 4	4/100 = 0.04
Democrat	98	200/2 = 100	(98 – 100)2 = 4	4/100 = 0.04
			χ2 = ∑[(O – E)2/E]	0.08

Degree of freedom: df = number of categories – 1 = 2 – 1 = 1

For significance of 0.05 and df = 1, χ² (table value) = 3.841

As χ² (calculated) < χ² (table value), there is significant reason to accept the null hypothesis.

There is no difference in the preference between republican versus democrat affiliation