Question

Before the presidential debates, it waa expected that the percentages of registered voters in favor of various candidates to be as follows.

Democrats 48%

Republicans 38%

Independent 04%

Undecided 10%

After the presidential debates, a random sample of 1200 voters showed that 540 favored the democrats candidate; 480 were in favor of the Republican candidate; 40 were in favor of the Independent candidate, and 140 were undecided. At 95% confidence, test to see if the proportion of voters has changed.

Answer 1

the expected frequency for each category is computed here as:

Ei = pi *1200

The chi square test statistic controbution for each category here is computed as:

	O_i	E_i	(O_i - E_i)^2/E_i
Democrats	540	576	2.25
Republicans	480	456	1.263157895
Independent	40	48	1.333333333
Undecided	140	120	3.333333333
	1200	1200	8.179824561

Therefore the chi square test statistic from the above table is computed here as:

For n - 1 = 3 degrees of freedom, the p-value here is computed from the chi square distribution tables as:

As the given p-value here is 0.04 < 0.05 which is the level of significance, therefore the test is significance here and we can reject the null hypothesis here and conclude that we have sufficient evidence that proportion of voters has changed.