Before the presidential debates, it was expected that the percentages of registe

Question

Before the presidential debates, it was expected that the percentages of registered voters in favor of various candidates to be as follows. Percentages Democrats 48% Republicans 38% Independent 4% Undecided 10% After the presidential debates, a random sample of 1200 voters showed that 540 favored the Democratic candidate; 480 were in favor of the Republican candidate; 40 were in favor of the Independent candidate, and 140 were undecided. At a 1% level of significance, test to see if the proportion of voters has changed. Calculate the value of the Chi-Square Test Statistic for this problem. What is it? Identify the critical value for this problem using the Table of Critical Values of the Chi Square Distribution in your text. What is the critical value?

Explanation / Answer

Ans:

Expected counts:

1200*0.48=576

1200*0.38=456

1200*0.04=48

1200*0.1=120

Test statistic:

Chi square=8.180

Critical chi square( for 0.01 significance level and df=3) =11.345

As,chi squre=8.180<11.345,we fail to reject null hypothesis.

We have sufficient evidence to suggest that proportion of voters has not changed.

Democrats republicans independent undecided Total Observed(O) 540 480 40 140 1200 Expected(E) 576 456 48 120 1200 (O-E)^2/E 2.250 1.263 1.333 3.333 8.180

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