Before the presidential debates, it was expected that the percentages of registered voters in favor of various candidates to be as follows. percent democrats 48% republicans 38% independent 04% 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 95% confidence, test to see if the proportion of voters has changed.

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(8.180,3,TRUE)"

Since the p value is lower than the significance level we can to reject the null hypothesis at 5% of significance, and we can conclude that we have significant differences in the proportions assumed.

Step-by-step explanation:

A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

The observed values are given by:

Democratic 540

Republican  480

Independent 40

Undecided   140

We need to conduct a chi square test in order to check the following hypothesis:

H0: There is no difference in the proportions for the political party

H1: There is a difference in the proportions for the political party

The level os significance assumed for this case is

The statistic to check the hypothesis is given by:

Now we just need to calculate the expected values with the following formula

And the calculations are given by:

And now we can calculate the statistic:

Now we can calculate the degrees of freedom for the statistic given by:

And we can calculate the p value given by:

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(8.180,3,TRUE)"

Since the p value is lower than the significance level we can to reject the null hypothesis at 5% of significance, and we can conclude that we have significant differences in the proportions assumed.

17   x 256=4352

sorry if this is wrong, i'm new.

step-by-step explanation: