Sure, let's determine the expected frequency for individuals with Blonde Hair and Blue Eyes based on the given data. We'll follow these steps:
1. Calculate the Marginal Totals:
- Calculate the total number of individuals with Blonde Hair:
- Blonde Hair Total = 25 (Blue) + 27 (Green) + 31 (Brown) = 83
- Calculate the total number of individuals with Blue Eyes:
- Blue Eyes Total = 25 (Blonde) + 26 (Brown) = 51
- Calculate the grand total of all individuals:
- Grand Total = (25 + 27 + 31) (Blonde) + (26 + 18 + 22) (Brown) = 149
2. Expected Frequency Calculation:
- The expected frequency for any cell in a contingency table is computed as:
[tex]\[
\text{Expected Frequency} = \frac{(\text{Row Total} \times \text{Column Total})}{\text{Grand Total}}
\][/tex]
- For Blonde Hair and Blue Eyes, we need:
[tex]\[
\text{Expected Frequency of Blonde Hair and Blue Eyes} = \frac{(\text{Total Blonde Hair} \times \text{Total Blue Eyes})}{\text{Grand Total}}
\][/tex]
- Plugging in the values we have:
[tex]\[
\text{Expected Frequency of Blonde Hair and Blue Eyes} = \frac{(83 \times 51)}{149}
\][/tex]
3. Perform the Multiplication and Division:
- Compute the value:
[tex]\[
\text{Expected Frequency of Blonde Hair and Blue Eyes} = \frac{4233}{149} \approx 28.41
\][/tex]
Thus, the expected frequency of Blonde Hair and Blue Eyes is approximately 28.41.
