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.

idk

step-by-step explanation:

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form