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A table represents the possibility of an association between hair color and eye color.

\begin{tabular}{|l|l|l|l|}
\hline & Eye Color & & \\
\hline Hair Color & Blue & Green & Brown \\
\hline Blonde & 25 & 27 & 31 \\
\hline Brown & 26 & 18 & 22 \\
\hline
\end{tabular}

In order to determine if the eye color of blue and blonde hair colors differ significantly, a chi-square test for homogeneity should be performed.

What is the expected frequency of Blonde Hair and Blue Eyes?

Answer choices are rounded to the nearest hundredth.



Answer :

GinnyAnswer
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.

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