The correct answer is False.
The pooled estimator is a weighted average of the group variances, where the weights are inversely proportional to the variances. This means that the group with the larger variance will have a smaller weight in the pooled estimator.
To understand why this is the case, consider the following example. Suppose we have two groups, each with 10 observations. The first group has a variance of 1, and the second group has a variance of 4. The pooled variance is then given by:
$$\frac{10 \times 1 + 10 \times 4}{10 + 10} = \frac{40}{20} = 2.$$
In this case, the group with the larger variance (group 2) has a weight of 0.5, which is half the weight of the group with the smaller variance (group 1). This is because the group with the larger variance is more likely to be an outlier, and we want to downweight the contribution of outliers in our estimate.
In general, the pooled estimator is a more robust estimate of the population variance than either of the individual group variances. This is because it is less sensitive to outliers.