An appropriate test to see whether the proportion of births for DATA2002 students is 0.25 for each of the 4 seasons is:

The appropriate test to determine whether the proportion of births for DATA2002 students is 0.25 for each of the 4 seasons is the Chi-Square Goodness of Fit test. Here are the steps to perform this test:

1. State the Hypotheses: The null hypothesis assumes that the proportion of births is the same for each season (0.25). The alternative hypothesis assumes that the proportion of births is not the same for each season.

2. Calculate the Expected Frequencies: If the null hypothesis is true, we would expect the number of births in each season to be 25% of the total number of births.

3. Calculate the Observed Frequencies: This is the actual data you have collected about the births in each season.

4. Calculate the Test Statistic: The test statistic is calculated using the formula for the Chi-Square statistic, which is the sum of the squared difference between the observed and expected frequencies, divided by the expected frequency, for each category (season).

5. Determine the P-value: The P-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. You can find this value using a Chi-Square distribution table or a statistical software.

6. Make a Decision: If the P-value is less than your chosen significance level (commonly 0.05), you reject the null hypothesis in favor of the alternative. If the P-value is greater than your chosen significance level, you do not reject the null hypothesis.

7. Interpret the Results: Based on your decision in step 6, you can make a conclusion about whether the proportion of births is the same for each season.