1. **Problem Statement:** We are performing a Chi-Square test to check if the observed frequencies of flower colors (Pink, White, Blue) fit the expected ratio 3:2:5 among 100 plants. 2. **Calculate Expected Frequencies:** - Total parts of ratio = 3 + 2 + 5 = 10 - Total plants = 100 - Expected Pink = $\frac{3}{10} \times 100 = 30$ - Expected White = $\frac{2}{10} \times 100 = 20$ - Expected Blue = $\frac{5}{10} \times 100 = 50$ 3. **Observed Frequencies:** - Pink (O) = 24 - White (O) = 14 - Blue (O) = 62 4. **Calculate Chi-Square Statistic ($\chi^2$):** $$\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$$ - Pink: $\frac{(24 - 30)^2}{30} = \frac{36}{30} = 1.2$ - White: $\frac{(14 - 20)^2}{20} = \frac{36}{20} = 1.8$ - Blue: $\frac{(62 - 50)^2}{50} = \frac{144}{50} = 2.88$ Sum: $$\chi^2 = 1.2 + 1.8 + 2.88 = 5.88$$ 5. **Degrees of Freedom ($df$):** $$df = \text{number of categories} - 1 = 3 - 1 = 2$$ 6. **Critical Value at 1% significance level ($\alpha=0.01$):** From Chi-Square distribution table, $$\chi^2_{critical, 0.01, 2} = 9.210$$ 7. **Conclusion:** - Calculated $\chi^2 = 5.88$ - Critical value $= 9.210$ Since $5.88 < 9.210$, we fail to reject the null hypothesis. **Interpretation:** The observed frequencies do not significantly differ from the expected ratio at 1% significance level. 8. **Software Analysis:** Using Python's scipy library: ```python import scipy.stats as stats observed = [24, 14, 62] expected = [30, 20, 50] chi2, p = stats.chisquare(f_obs=observed, f_exp=expected) print(f"Chi2 Statistic: {chi2}, p-value: {p}") ``` The p-value > 0.01 supports the conclusion that observed data fits expected ratio.