Question

1. Calculate the appropriate percentages for bivariate analysis and provide a brief summary of the relationship between education and divorce using the method of comparing percentage differences discussed in the chapter and in class.

   	Highest Degree
   Ever Been Divorced	School	High School	Junior College	Bachelors Degree	Graduate Degree
   Yes	107	362	55	89	52
   No	285	867	149	374	195

Answer 1

Solution:-

Percentage

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

H0: Relationship and education are independent.

Ha: Relationship and education 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.

DF = (r - 1) * (c - 1) = (5 - 1) * (2 - 1)

D.F = 4

Er,c = (nr * nc) / n

Χ2 = Σ [ (Or,c - Er,c)2 / Er,c ]

Χ2 = 78.4

where DF is the degrees of freedom.

The P-value is the probability that a chi-square statistic having 4 degrees of freedom is more extreme than 22.06

We use the Chi-Square Distribution Calculator to find P(Χ2 > 22.06) = 0.0002

Interpret results. Since the P-value (0.0002) is less than the significance level (0.05), we cannot accept the null hypothesis. Thus, we conclude that there is a relationship between Relationship and education.