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.
(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.
1 answer