Question

In the following table, The independent variable is_______________ , and the dependent variable is_____________ What is the null and the alternative hypotheses?  Running a chi-square analysis, you obtain a chi-square value of 22.9 with a significance level of <0.000, which hypothesis (null or alternative) should you, therefore, choose as correct?  Can you estimate a directionalmeasure of association between these two variables? Why or why not?

                                                                                   Sex

Political party	Male	female	Total
Democrat	179	312	491
Republican	273	347	620
Independent	183	173	356
Other party	15	10	25
Total	650	842	1492

Answer 1

Solution:-

The independent variable is gender , and the dependent variable is political party.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

H₀: Gender and political party are independent.
H_a: Gender and political party are not independent.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square test for independence.

Analyze sample data. Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

1) The sampling method is simple random sampling.

2) The variables under study are each categorical.

3) If sample data are displayed in a contingency table, the expected frequency count for each cell of the table is at least 5.

DF = (r - 1) * (c - 1) = (2 - 1) * (4 - 1)
D.F = 3
E_r,c = (n_r * n_c) / n

Χ² = 22.9

where DF is the degrees of freedom.

The P-value is the probability that a chi-square statistic having 3 degrees of freedom is more extreme than 22.9.

We use the Chi-Square Distribution Calculator to find P(Χ² > 22.9) = 0.00.

Interpret results. Since the P-value (0.00) is less than the significance level (0.05), we have to reject the null hypothesis. Thus, we conclude that there is a relationship between gender and political party.

We can not estimate a directional measure of association between these two variables.