Assume That $\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 } = \sigma ^ { 2 }$

Essay

Assume that $\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 } = \sigma ^ { 2 }$ . Calculate the pooled estimator of $\sigma ^ { 2 }$ for $s _ { 1 } ^ { 2 } = 50$ , $s _ { 2 } ^ { 2 } = 57$ , and $n _ { 1 } = n _ { 2 } = 18$ .