A Paired Difference Experiment Yielded the Following Results $$n _ { d } = 50 , \Sigma ^ { d } = 967 , \Sigma ^ { d ^ { 2 } } = 19,201$$

Essay

A paired difference experiment yielded the following results. $$n _ { d } = 50 , \Sigma ^ { d } = 967 , \Sigma ^ { d ^ { 2 } } = 19,201$$
Test $H _ { 0 } : \mu _ { d } = 20$ against $H _ { \mathrm { a } } : \mu _ { d } \neq 20$ , where $\mu _ { d } = \mu _ { 1 } ^ { \prime } \mu _ { 2 }$ , using $\alpha = .05$ .