Biology – Variation | e-Consult

Hypothesis:

• Null Hypothesis (H₀): There is no significant difference in the mean height of plants treated with the new fertilizer compared to the control group. (μ_fertilizer = μ_control)
• Alternative Hypothesis (H₁): There is a significant difference in the mean height of plants treated with the new fertilizer compared to the control group. (μ_fertilizer ≠ μ_control)

Test Statistic:

The t-statistic is calculated as follows: t = (x̄_fertilizer - x̄_control) / (s_p / √n_fertilizer + s_p / √n_control)

Where:

• x̄_fertilizer = Sample mean height of the fertilizer group (calculated as 18.87 cm)
• x̄_control = Sample mean height of the control group (calculated as 16.93 cm)
• s_p = Pooled standard deviation
• n_fertilizer = Sample size of the fertilizer group (20)
• n_control = Sample size of the control group (22)

Calculating the pooled standard deviation (s_p):

s_p = √[((n_fertilizer - 1)s_fertilizer² + (n_control - 1)s_control²) / (n_fertilizer + n_control - 2)]

Assuming the standard deviations are equal (which is a reasonable assumption for a t-test), we can calculate the t-statistic. The provided t-value of 1.96 suggests that the calculated t-statistic, when compared to the degrees of freedom (df = n_fertilizer + n_control - 2 = 20 + 22 - 2 = 40), results in a p-value of 0.05.

Conclusion:

Since the p-value (0.05) 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 height of plants treated with the new fertilizer compared to the control group. Specifically, the fertilizer appears to increase plant height.