Answer: The pooled estimate for a common population variance is approximately 9.52.
Explanation:
To find the pooled estimate for a common population variance, we can use the formula:
Pooled Variance = [(n1-1) * Var1 + (n2-1) * Var2] / (n1 + n2 - 2)
In this case, the first sample has a size of 15 and a variance of 8.6, while the second sample has a size of 20 and a variance of 10.2.
Using the formula, we can calculate the pooled estimate for the common population variance as follows:
Pooled Variance = [(15-1) * 8.6 + (20-1) * 10.2] / (15 + 20 - 2)
Pooled Variance = (14 * 8.6 + 19 * 10.2) / (33)
Pooled Variance = (120.4 + 193.8) / 33
Pooled Variance = 314.2 / 33
Pooled Variance ≈ 9.52
Therefore, the pooled estimate for a common population variance is approximately 9.52.
I hope this helps :)