1. **Stating the problem:** We want to perform an inferential statistical study to understand how students cope with stress based on the given bar graph data. 2. **Data summary:** The data shows frequencies and percentages of students using different coping mechanisms out of a total of 112 responses: - Exercising: 28 (25%) - Talking with family/friends: 17 (15%) - Listing out/journaling: 28 (25%) - Seeking professional help: 2 (2%) - Going out: 10 (9%) - Playing games/Watching YouTube: 17 (15%) - Others: 13 (12%) 3. **Objective:** We want to test if the coping mechanisms are equally preferred by students or if some are significantly more common. 4. **Hypotheses:** - Null hypothesis $H_0$: All coping mechanisms are equally preferred, i.e., the proportions are equal. - Alternative hypothesis $H_a$: At least one coping mechanism has a different preference proportion. 5. **Test used:** Chi-square goodness-of-fit test. 6. **Expected frequencies:** If all 7 categories were equally preferred, expected frequency per category is $$E = \frac{112}{7} = 16$$. 7. **Calculate chi-square statistic:** $$\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$$ where $O_i$ is observed frequency and $E_i$ is expected frequency. Calculate each term: - Exercising: $\frac{(28-16)^2}{16} = \frac{144}{16} = 9$ - Talking: $\frac{(17-16)^2}{16} = \frac{1}{16} = 0.0625$ - Listing out: $\frac{(28-16)^2}{16} = 9$ - Seeking help: $\frac{(2-16)^2}{16} = \frac{196}{16} = 12.25$ - Going out: $\frac{(10-16)^2}{16} = \frac{36}{16} = 2.25$ - Playing games: $\frac{(17-16)^2}{16} = 0.0625$ - Others: $\frac{(13-16)^2}{16} = \frac{9}{16} = 0.5625$ Sum: $$\chi^2 = 9 + 0.0625 + 9 + 12.25 + 2.25 + 0.0625 + 0.5625 = 33.1875$$ 8. **Degrees of freedom:** $df = k - 1 = 7 - 1 = 6$ 9. **Decision rule:** Using chi-square distribution table, critical value for $\alpha=0.05$ and $df=6$ is approximately 12.592. 10. **Conclusion:** Since $33.1875 > 12.592$, we reject the null hypothesis. **Interpretation:** There is significant evidence that students do not equally prefer all coping mechanisms; some are more commonly used than others. This inferential study helps us understand the distribution of coping strategies among students and guides where support or resources might be focused.