Differentiate between goodness of fit test and contingency chi square test. In a study of 200 married women, a researcher tried to establish if there is an association between marital status and job affiliation. He obtained the following data:

• Null Hypothesis ($H_0$): There is no association between marital status and job affiliation. (Marital status and job affiliation are independent).
• Alternative Hypothesis ($H_1$): There is an association between marital status and job affiliation. (Marital status and job affiliation are not independent).

The formula for expected frequency is $E_{ij} = \frac{(\text{Row Total}_i) \times (\text{Column Total}_j)}{\text{Grand Total}}$.

• $E_{\text{Married, Civil Servant}} = \frac{93 \times 87}{200} = 40.455$
• $E_{\text{Married, Traders}} = \frac{93 \times 42}{200} = 19.53$
• $E_{\text{Married, Farmers}} = \frac{93 \times 71}{200} = 33.015$
• $E_{\text{Single, Civil Servant}} = \frac{70 \times 87}{200} = 30.45$
• $E_{\text{Single, Traders}} = \frac{70 \times 42}{200} = 14.7$
• $E_{\text{Single, Farmers}} = \frac{70 \times 71}{200} = 24.85$
• $E_{\text{Separated, Civil Servant}} = \frac{37 \times 87}{200} = 16.095$
• $E_{\text{Separated, Traders}} = \frac{37 \times 42}{200} = 7.77$
• $E_{\text{Separated, Farmers}} = \frac{37 \times 71}{200} = 13.135$

The formula is $\chi^2 = \sum \frac{(O_{ij} - E_{ij})^2}{E_{ij}}$.

Where r = number of rows (marital statuses = 3) and c = number of columns (job affiliations = 3).

Assuming a significance level ($\alpha$) of 0.05 (standard if not specified).
For $df = 4$ and $\alpha = 0.05$, the critical $\chi^2$ value is 9.488.

Compare the calculated $\chi^2$ value with the critical $\chi^2$ value.
Calculated $\chi^2 = 17.0285$
Critical $\chi^2 = 9.488$
Since $17.0285 > 9.488$, we reject the null hypothesis.

There is sufficient evidence at the 0.05 significance level to conclude that there is a significant association between marital status and job affiliation.