Biology – Variation | e-Consult

Hypothesis:

• Null Hypothesis (H₀): There is no significant difference in the mean number of insects between Area A and Area B. (μ_A = μ_B)
• Alternative Hypothesis (H₁): There is a significant difference in the mean number of insects between Area A and Area B. (μ_A ≠ μ_B)

Test Statistic:

The t-statistic is calculated as follows: t = (x̄_A - x̄_B) / (s_p / √n_A + s_p / √n_B)

Where:

• x̄_A = Sample mean number of insects in Area A (125)
• x̄_B = Sample mean number of insects in Area B (110)
• s_p = Pooled standard deviation
• n_A = Sample size of Area A (n = 10)
• n_B = Sample size of Area B (n = 10)

The provided t-value of 2.12, with degrees of freedom (df = n_A + n_B - 2 = 10 + 10 - 2 = 18), and a p-value of 0.02 indicates a statistically significant difference.

Conclusion:

Since the p-value (0.02) is less than the significance level (0.05), we reject the null hypothesis. There is statistically significant evidence to suggest that there is a difference in the mean number of insects between Area A and Area B. The pesticide use in Area A appears to lead to a higher insect population.