Let $X _ { 1 } , X _ { 2 } , \ldots \ldots , X _ { 40 }$

Let $X _ { 1 } , X _ { 2 } , \ldots \ldots , X _ { 40 }$ be a random sample from a normal population with mean $\mu _ { 1 }$ and variance $\sigma _ { 1 } ^ { 2 } = 2.56 \text {, and let } Y _ { 1 } , Y _ { 2 } , \ldots \ldots Y _ { 32 }$ be a random sample from a normal population with mean $\mu _ { 2 } \text { and variance } \sigma _ { 2 } ^ { 2 } = 1.96 \text {, }$ and that X and Y samples are independent of one another. Assume the sample mean values are $\bar { x } = 18 \text { and } \bar { y } = 17$ and we want to test $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0 \text { versus } H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } > 0 \text {. }$ Which of the following statements are correct?

A) The value of the test statistic is z = 2.83
B) The value of the test statistic is z = 1.88
C) $H _ { o }$
Is rejected at the .05 level if $z \leq 1.96$
D) $H _ { o }$
Is rejected at the .05 level if $z \leq 1.65$
E) None of the above statements are correct.