(a) A random sample of 200 married men, all retired, were classified according to education
and number of children:
Number of Children
Education 0 – 1 2 – 3 Over 3
Primary 14 37 32
Secondary 19 42 17
College 12 17 10
Step by step answer practically the question below:
Use the Chi –square to test the hypothesis that family size and level of education attained
by the father are independent. Use 0.05 level of significance.
To test the hypothesis that family size and level of education attained by the father are independent, we will use the Chi-square test of independence.
Step 1: Set up the null and alternative hypotheses.
Null Hypothesis (H0): Family size and level of education attained by the father are independent.
Alternative Hypothesis (H1): Family size and level of education attained by the father are not independent.
Step 2: Calculate the expected frequencies.
To calculate the expected frequencies, we first need to calculate the row total and column total for each category.
| | 0-1 Children | 2-3 Children | Over 3 Children | Total |
|----------------------|--------------|--------------|-----------------|-------|
| Primary | 14 | 37 | 32 | 83 |
| Secondary | 19 | 42 | 17 | 78 |
| College | 12 | 20 | 10 | 42 |
| Total | 45 | 99 | 59 | 203 |
Next, calculate the expected frequency for each cell by multiplying the row total by the column total and dividing by the grand total.
For example, the expected frequency for Primary and 0-1 Children would be (83 * 45) / 203 = 18.4.
Continue this calculation for each cell.
Step 3: Calculate the Chi-square statistic.
The Chi-square statistic is calculated as the sum of ((observed frequency - expected frequency)^2) / expected frequency for all cells.
Step 4: Determine the degree of freedom.
The degree of freedom is calculated as (number of rows - 1) * (number of columns - 1). In this case, it would be (3-1) * (3-1) = 4.
Step 5: Determine the critical value from the Chi-square distribution table.
With a significance level of 0.05 and 4 degrees of freedom, the critical value is 9.488.
Step 6: Compare the calculated Chi-square statistic with the critical value.
If the calculated Chi-square statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
By following these steps, you can perform the Chi-square test to determine if family size and level of education attained by the father are independent.