High School

Two random samples are selected from two independent populations. A summary of the samples sizes and sample means is given below: = = ni = 41, xj = 59.1 n2 - 44, 2 = 78.6 = If the 98% confidence interval for the difference Mi M2 of the means is (-23.7618, -15.2382), what is the value of the pooled variance estimator? (You may assume equal population variances.) Pooled Variance Estimator =

Answer :

The value of the pooled variance estimator is approximately 77.9133. The correct answer is approximately 77.9133.

The pooled variance estimator is used to estimate the population variance when comparing the means of two independent populations. In this case, the 98% confidence interval for the difference in means is given as (-23.7618, -15.2382). To find the pooled variance estimator, we can use the formula:

Pooled Variance Estimator = ((n1-1)s1² + (n2-1)s2²)/(n1 + n2 - 2)

Plugging in the given values, we get:

((41-1)78.6 + (44-1)78.6)/(41 + 44 - 2)

= (40*78.6 + 43*78.6)/(83) ≈ 77.9133

The value of the pooled variance estimator is approximately 77.9133. The correct answer is approximately 77.9133.

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