Answer: 1.96

## Explanation This question involves testing the equality of variances between two populations (pharmaceutical stocks and e-commerce stocks). The appropriate statistical test for comparing variances is the **F-test**. ### Formula for F-test statistic: \[ F = \frac{s_1^2}{s_2^2} \] Where: - \( s_1 \) = standard deviation of sample 1 - \( s_2 \) = standard deviation of sample 2 ### Given data: - Pharmaceutical stocks standard deviation = 1.50% - E-commerce stocks standard deviation = 2.10% ### Calculation: \[ F = \frac{(2.10\%)^2}{(1.50\%)^2} = \frac{0.021^2}{0.015^2} = \frac{0.000441}{0.000225} = 1.96 \] ### Important convention: In practice, it's conventional to place the **larger variance in the numerator** so that the F-statistic is always ≥ 1. This simplifies hypothesis testing since we only need to look at the right tail of the F-distribution. ### Why other options are incorrect: - **A. 1.51**: This might result from incorrectly calculating \( \frac{2.10}{1.50} \) instead of the ratio of variances - **C. 1.70**: This doesn't correspond to any logical calculation from the given data - **D. 2.14**: This might result from calculating \( \frac{1.50}{2.10} \) and then taking the reciprocal incorrectly The correct test statistic value is **1.96**, which corresponds to option B.

Author: Nikitesh Somanthe