Question

One sample has Aa Aa One sample has n 10 scores and a variance of s2 20, and a second sample has n 15 scores and a variance of s2 30. What can you conclude about the pooled variance for these two samples? a. It will be closer to 30 than to 20 b. Cannot be determined from the information given. c. It will be closer to 20 than to 30. d. It will be exactly halfway between 20 and 30.

Answer 1

Answer:

option (a) It will be closer to 30 than to 20

Step-by-step explanation:

Data provided in the question:

For sample 1:

n₁ = 10

variance, s₁² = 20

For sample 2:

n₂ = 15

variance, s₂² = 30

Now,

The pooled variance is calculated using the formula,

$S^{2}_{p} = \frac{(n_{1}-1)\times s^{2}_{1} +(n_{2}-1)\times s^{2}_{2}}{n_{1}+n_{2}-2}$

on substituting the given respective values, we get

$S^{2}_{p} = \frac{(10-1)\times 20 +(15-1)\times 30}{10+15-2}$

or

$S^{2}_{p}$ = 26.0869

Hence,

the pooled variance will be closer to 30 than to 20

Therefore,

The correct answer is option (a) It will be closer to 30 than to 20