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The image you provided contains a statistical problem with a contingency table related to hypothesis testing. The question involves analyzing whether there is a significant difference between groups using a statistical test, likely a Chi-square test given the format.

Let's break down the problem step by step:

### Step 1: Understanding the Contingency Table
The table provided is structured as follows:

| Kategori      | Prodi S1 Akuntansi | Prodi S1 Manajemen | Prodi D3 Akuntansi | Prodi D3 Perdagangan | Total |
|---------------|--------------------|--------------------|--------------------|----------------------|-------|
| Sangat layak  | 20                 | 25                 | 10                 | 20                   | 75    |
| Layak         | 40                 | 50                 | 40                 | 45                   | 175   |
| Tidak layak   | 10                 | 25                 | 10                 | 30                   | 75    |
| Total         | 70                 | 100                | 60                 | 95                   | 325   |

### Step 2: Hypothesis Formulation
1. **Null Hypothesis (H₀):** There is no significant difference in the evaluation (Sangat layak, Layak, Tidak layak) across the different programs (Prodi S1 Akuntansi, Prodi S1 Manajemen, etc.).
2. **Alternative Hypothesis (H₁):** There is a significant difference in the evaluation across the different programs.

### Step 3: Chi-square Test Calculation
To perform the Chi-square test, follow these steps:
1. **Calculate the Expected Frequencies:**
   \[
   E_{ij} = \frac{(Row\ Total)_i \times (Column\ Total)_j}{Grand\ Total}
   \]
   For example, the expected frequency for "Sangat layak" in "Prodi S1 Akuntansi" is:
   \[
   E_{11} = \frac{75 \times 70}{325} = \frac{5250}{325} = 16.15
   \]

2. **Compute Chi-square Statistic:**
   \[
   \chi^2 = \sum \frac{(O_{ij} - E_{ij})^2}{E_{ij}}
   \]
   Where \( O_{ij} \) is the observed frequency and \( E_{ij} \) is the expected frequency.

3. **Determine Degrees of Freedom (df):**
   \[
   df = (r-1) \times (c-1)
   \]
   Where \( r \) is the number of rows and \( c \) is the number of columns.

4. **Compare Chi-square Statistic with Critical Value:**
   Use the chi-square distribution table to find the critical value at the desired significance level (e.g., α = 0.05).

### Step 4: Decision
- If \( \chi^2 \) calculated > \( \chi^2 \) table value, reject the null hypothesis.
- Otherwise, fail to reject the null hypothesis.

### Step 5: Interpretation
This step involves interpreting the results in the context of the problem.

### Next Steps
Would you like me to perform the detailed calculation of the Chi-square test for this problem, including all intermediate steps and expected frequencies?

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**Next Relative Questions:**

1. How do you calculate the expected frequencies in a contingency table?
2. What are the degrees of freedom in a Chi-square test?
3. How do you determine the critical value in a Chi-square test?
4. What does it mean if the Chi-square statistic is greater than the critical value?
5. How would you interpret the results of this Chi-square test?

**Tip:** Always check the assumptions of the Chi-square test, such as the expected frequency in each cell being greater than 5, to ensure the validity of the test.

Learn how to analyze a statistical problem involving a contingency table and hypothesis testing using the Chi-square test. This problem covers detailed steps for calculating expected frequencies and interpreting Chi-square statistics. Suitable for advanced high school or college students.

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