Suppose $\mu _ { 1 } \text { and } \mu _ { 2 }$

Essay

Suppose $\mu _ { 1 } \text { and } \mu _ { 2 }$ are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. Use the two-sample $t$ test at significance level .01 to test $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = - 10 \text { versus } H _ { a } : \mu _ { 1 } - \mu _ { 2 } < - 10$ for the following statistics: $m = 6 , \bar { x } = 116 , s _ { 1 } = 5.0 , n = 6 , \bar { y } = 129 , \text { and } s _ { 2 } = 5.5$