It looks like you're working on a problem involving the computation of expected frequencies under the null hypothesis in a test for independence. From the image, I see the table lists expected frequencies for different categories of "Siblings" and "Number of Children."

The problem asks you to compute the expected frequencies and fill in the missing values in the table, which will require the application of the formula for expected frequency in contingency tables:

$E_{ij} = \frac{(Row \ Total) \times (Column \ Total)}{Grand \ Total}$

Where:

• $E_{ij}$ is the expected frequency for the cell in the $i$-th row and $j$-th column,
• Row Total is the sum of the frequencies in that row,
• Column Total is the sum of the frequencies in that column,
• Grand Total is the sum of all the frequencies in the table.

To complete the table, you will need to find the missing expected values based on the totals.

Would you like me to help walk you through a specific example or clarify how to calculate one of the missing frequencies?

Here are 5 related questions:

1. How do you calculate row and column totals for a contingency table?
2. What is the significance of expected frequencies in a Chi-square test for independence?
3. Can you explain how to interpret the results of a Chi-square test once expected and observed frequencies are compared?
4. How do rounding errors impact statistical calculations like the Chi-square test?
5. What are the assumptions behind using a Chi-square test for independence?

Tip: Always double-check that the sum of your calculated expected frequencies matches the grand total for consistency!