A political scientist wanted to learn whether there is any...

A political scientist wanted to learn whether there is any association between the education level of a registered voter and his or her political party affiliation. He randomly selected 46 registered voters and obtained the following data: (a) Construct a contingency table for the two variables. (b) Test whether level of education is independent of political affiliation at the $\alpha=0.1$ level of significance. (c) Construct a conditional distribution of political party by level of education and draw a bar graph. Does this evidence support your conclusion in part (b)? (TABLE CAN'T COPY)

A political scientist wanted to learn whether there is any association between the education level of a registered voter and his or her political party affiliation. He randomly selected 46 registered voters and obtained the following data:
(a) Construct a contingency table for the two variables.
(b) Test whether level of education is independent of political affiliation at the $\alpha=0.1$ level of significance.
(c) Construct a conditional distribution of political party by level of education and draw a bar graph. Does this evidence support your conclusion in part (b)?
(TABLE CAN'T COPY)

Key Concepts

Data Visualization - Bar Graphs

Bar graphs are used to visually display and compare the frequencies or proportions of categories within one or more groups. In the context of conditional distributions, side-by-side or clustered bar graphs can effectively illustrate how the distribution of one categorical variable changes across different levels of another variable, aiding in the interpretation of the association assessed through statistical tests.

Conditional Distribution

A conditional distribution shows how the values of one categorical variable are distributed within the levels of another categorical variable. It provides insight into the behavior of one variable given that the other variable is fixed at a particular level, which helps in understanding the nature of the association between the two variables.

Hypothesis Testing and Significance Level

Hypothesis testing in a categorical setting involves setting up a null hypothesis that assumes no association between the variables (i.e., independence) and an alternative hypothesis that suggests an association exists. The significance level (alpha) is the predetermined threshold for determining whether the observed test statistic is extreme enough to reject the null hypothesis, traditionally set at levels such as 0.05 or 0.1.

Contingency Table

A contingency table is a tabular method used to display the frequency distribution of two categorical variables. It arranges data into rows and columns corresponding to the categories of each variable. This structure allows for the easy calculation of marginal totals and provides a clear overview for identifying potential relationships or associations between the variables.

Chi-square Test of Independence

The Chi-square test of independence is a statistical method used to determine whether there is a significant association between two categorical variables. It involves comparing the observed frequencies in each cell of a contingency table with the expected frequencies calculated under the assumption that the variables are independent. The resulting test statistic follows a Chi-square distribution with degrees of freedom determined by the number of categories in each variable.

Transcript

00:01 In this question, we are given with the data on political party, accreditation and educational level of the respondents.

00:18 So we, in the first part of the question, we are asked to construct a contingency table using the information given in the question.

00:27 So using the information, we saw that there are seven individuals who has a great school education and are democrat and two are republican.

00:46 High school education, those who has high school education, 10 of them are democrat and six are republican.

00:57 Nine individuals are affiliated with democrat political party and has college education and 12 are republicans and college education.

01:12 So this is the contingency table.

01:14 We use the information given in the question and constructed this contingency table.

01:20 We will compute the row total and column total for this table and the crane total.

01:28 So that we can use these information later in competition section.

01:36 So in the first, the second part of the question we are asked to test whether education is independent of political affiliation.

01:44 So our h.

01:45 Not will be education is not independent of political affiliation and our one will be education is independent of critical affiliation.

01:54 We are asked to test this hypothesis 8.

01:59 0 .1 level of significance sorry it is 0 .0 .0 .0 .0 .1 it's 0 .1 level of significance and 0 .1.

02:17 And we will use kai square test of independence to check this evaluation, to test our non -hypothesis.

02:26 So as we know that the kai square statistics is kai square is kai -square of observed oi over here is observed values which have given in the table minus expected value which we will compute the square divided by expected value with r minus one and c minus one degree of freedom r is number of raws c is number of columns so r minus one raw minus one column minus one is equal to two the product is two so in the formula um in the test statistics given about oi is observed value which are given in the table and and ei is expected value, which we will compute by multiplying the raw total, multiply by column total divided by green total.

03:09 Like going back to the table, our first observation is seven.

03:14 This is observed value...

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