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This image presents a Chi-Square test of independence for attitudes towards online classes among 600 respondents. The test compares observed values (O) and expected values (E) for three attitude categories ("Yes," "Neutral," and "No") and calculates the Chi-Square statistic (χ²) using the formula:

\[
\chi^2 = \sum \frac{(O - E)^2}{E}
\]

Here's a breakdown of the calculations:

1. **Observed values (O)**:
   - Yes: 250
   - Neutral: 200
   - No: 150
   - Total: 600

2. **Expected values (E)**: Since there are 600 respondents divided evenly across three categories, each expected value is \( \frac{600}{3} = 200 \).

3. **Difference (O - E)**:
   - Yes: \( 250 - 200 = 50 \)
   - Neutral: \( 200 - 200 = 0 \)
   - No: \( 150 - 200 = -50 \)

4. **Square of Differences \((O - E)^2\)**:
   - Yes: \( 50^2 = 2500 \)
   - Neutral: \( 0^2 = 0 \)
   - No: \((-50)^2 = 2500 \)

5. **Calculating \((O - E)^2 / E\)**:
   - Yes: \( \frac{2500}{200} = 12.5 \)
   - Neutral: \( \frac{0}{200} = 0 \)
   - No: \( \frac{2500}{200} = 12.5 \)

6. **Total Chi-Square Value (Computed Value)**:
   \[
   \chi^2 = 12.5 + 0 + 12.5 = 25
   \]

### Hypotheses
- **Null Hypothesis (H₀)**: There is no significant association between the attitude of the respondents and their online classes.
- **Alternative Hypothesis (Hₐ)**: There is a significant association between the attitude of the respondents and their online classes.

### Degree of Freedom (df)
For a Chi-Square test of independence with \(k\) categories, the degrees of freedom are calculated as:
\[
df = k - 1 = 3 - 1 = 2
\]

### Summary
The computed Chi-Square value is 25, which would be compared to a critical Chi-Square value from a Chi-Square distribution table for 2 degrees of freedom to determine if the null hypothesis should be rejected.

Would you like more details on interpreting this result or performing further steps?

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1. How can you find the critical Chi-Square value at a specific significance level?
2. What is the interpretation if the computed Chi-Square value exceeds the critical value?
3. How would you interpret the result if the null hypothesis cannot be rejected?
4. How can you calculate expected values for cases with more categories?
5. What adjustments are necessary if the data categories are uneven?

**Tip**: Always check your degrees of freedom and sample size before interpreting Chi-Square results, as they affect the critical value significantly.

Perform a Chi-Square test of independence for attitudes towards online classes among 600 respondents.

This solution demonstrates the Chi-Square test of independence for analyzing attitudes towards online classes among 600 respondents. Learn how to calculate the Chi-Square value with observed and expected frequencies, hypothesis formulation, and degrees of freedom.

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