We are tasked with calculating the expected value for the number of doctors voting for the Democratic party using a contingency table for a chi-square test of independence.

Given dataWe are tasked with calculating the expected value for the number of doctors voting for the Democratic party using a contingency table for a chi-square test of independence.

Given

We are asked to compute the expected value for the number of doctors voting for the Democratic party.

Formula for Expected Value:

The formula to calculate the expected value $E_{ij}$ for a cell in a contingency table is:

$E_{ij} = \frac{(\text{Row Total of } i) \times (\text{Column Total of } j)}{\text{Grand Total}}$

Here:

• Row total for doctors: 67
• Column total for Democrats: 175
• Grand total: 295

Substituting these values into the formula:

$E_{Doctor, Democrat} = \frac{67 \times 175}{295}$

Let's calculate that.The expected value for the number of doctors voting for the Democratic party is approximately 39.745763.

Would you like further details or have any questions about the calculations?

Here are some related questions:

1. How do we interpret the chi-square test of independence?
2. What is the next step in conducting the full chi-square test for this data?
3. How do you compute the chi-square statistic for the entire table?
4. What is the significance level and how is it applied in hypothesis testing?
5. Can this test determine causation or just association?

Tip: Always ensure the assumptions of a chi-square test are met, such as having expected frequencies greater than 5 in each cell.