A study of voting preferences among enlisted soldiers (of differing educational levels) in the military reveals the follow patterns (the sample size if 445).
1 Of 395 high school graduates, 90 describe themselves as Democrats, 170 as Independents, and 135 as Republicans
2 Of 27 college graduates, 3 describe themselves as Democrats, 18 as Independents, and 6 as Republicans
3 Of 23 who did not complete high school, 7 describe themselves as Democrats, 7 as Independents, and 9 as Republicans
Using the six-step hypothesis-testing framework from class, please test for independence between the level of education and political party affiliation. Set the level of significance at .05.
You can do a chi-square test to determine if the variables are related or unrelated in the population. The null hypothesis states the variables are unrelated in the population. The alternate or alternative hypothesis states the variables are related in the population. The purpose of a chi-square test is to determine if two or more variables are independent of each other (the null hypothesis) or are dependent (the alternate or alternative hypothesis). If the null is rejected, you can conclude that the variables are related in some manner or connected in some way. If the null is not rejected, you cannot conclude that the variables are related.
Dear Math Guru,
Can you please help me how to use the chi square formula
To test for independence between the level of education and political party affiliation, we can conduct a chi-square test of independence. This test assesses whether there is a relationship between two categorical variables.
Step 1: State the Null Hypothesis (H0)
The null hypothesis states that there is no association between the level of education and political party affiliation.
H0: The level of education and political party affiliation are independent.
Step 2: State the Alternative Hypothesis (H1)
The alternative hypothesis states that there is an association between the level of education and political party affiliation.
H1: The level of education and political party affiliation are not independent.
Step 3: Set the Significance Level (α)
The significance level is given as 0.05.
Step 4: Create the Contingency Table
We need to create a contingency table that displays the observed frequencies for each combination of education level and political party affiliation.
Democrats Independents Republicans
-------------------------------------------------------------
High School 90 170 135
College 3 18 6
Did Not Complete 7 7 9
High School E1 E2 E3
Total 100 195 150
Step 5: Calculate the Expected Frequencies
We need to calculate the expected frequencies for each cell of the contingency table under the assumption of independence between the variables.
To calculate the expected frequency for each cell, we use the formula: (row total * column total) / sample size.
For example, the expected frequency for the cell in the first row and first column (Democrats among high school graduates) would be:
(395 * 100) / 445 = 88.7
By following this formula, we calculate the expected frequencies for all the cells.
Step 6: Perform the Chi-Square Test
We can now perform the chi-square test using the contingency table with observed and expected frequencies. The test statistic is calculated as:
X^2 = Σ [(O - E)^2 / E]
where O is the observed frequency, E is the expected frequency, and Σ refers to summing over all cells.
Using the calculated test statistic, we compare it to the critical value from the chi-square distribution with degrees of freedom equal to (number of rows - 1) * (number of columns - 1). If the test statistic is greater than the critical value, we reject the null hypothesis.
Once the critical value is determined, and you have calculated the test statistic, you can conclude whether there is evidence to reject or fail to reject the null hypothesis (H0).
I hope this explanation helps you understand how to test for independence between the level of education and political party affiliation using the chi-square test of independence.