Consider a study in which the population variance estimate based on treatment group of 14 participants is 8, and the population variance estimate based on a control group of 17 individuals is 9.
Compute the pooled estimate of population variance.
- 7.25
- 8.55
- 9.22
- 10.05
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7.25
To compute the pooled estimate of population variance, you need to use the formula for pooled variance, which takes into account the variances and sample sizes of the treatment and control groups.
The formula for pooled variance is:
Pooled Variance = [(n1-1)*s1^2 + (n2-1)*s2^2] / (n1 + n2 - 2)
Where:
- n1 is the sample size of the treatment group
- s1^2 is the variance estimate based on the treatment group
- n2 is the sample size of the control group
- s2^2 is the variance estimate based on the control group
In this case, the sample size of the treatment group is 14 and the variance estimate is 8, while the sample size of the control group is 17 and the variance estimate is 9.
Using the formula, we can calculate the pooled variance:
Pooled Variance = [(14-1)*8 + (17-1)*9] / (14 + 17 - 2)
= (13*8 + 16*9) / 29
= (104 + 144) / 29
= 248 / 29
= 8.55
Therefore, the correct answer is option - 8.55.