Let $X _ { 1 } , X _ { 2 } , \ldots \ldots , X _ { 20 }$

Let $X _ { 1 } , X _ { 2 } , \ldots \ldots , X _ { 20 }$ be a random sample from a normal population with mean $\mu _ { 1 } \text { and variance } σ _ { 1 } ^ { 2 } = 25 \text {, and let } Y _ { 1 } , Y _ { 2 } , \ldots \ldots , Y _ { 25 }$ be a random sample from a normal population with mean $\mu _ { 1 } \text { and variance } \sigma _ { 1 } ^ { 2 } = 25 \text {, and let } Y _ { 1 } , Y _ { 2 } , \ldots \ldots , Y _ { 25 }$ be a random sample from a normal population with mean $\mu _ { 2 } \text { and variance } \sigma _ { 2 } ^ { 2 } \text {, }$ =16, and that X and Y samples are independent of one another. If the sample mean values are $\bar { x } = 30 \text { and } \bar { y } = 32$ then the value of the test statistic to test $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0 \text { versus } H _ { \Delta } : \mu _ { 1 } - \mu _ { 1 } \neq 0$ is z = __________ and that $H _ { o }$ will be rejected at .01 significance level if $z \geq$$\underline{\quad\quad}$ or $z \leq$$\underline{\quad\quad}$