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

Essay

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