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.