A Researcher Wishes to Determine Whether People with High Blood $99 \%$

A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by following a particular diet. Use the sample data below to construct a $99 \%$ confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ where $\mu _ { 1 }$ and $\mu _ { 2 }$ represent the mean for the treatment group and the control group respectively.
Treatment Group: $n _ { 1 } = 85 , \bar { Y } _ { 1 } = 189.1 , s _ { 1 } = 38.7$
Control Group: $n _ { 2 } = 75 , \bar { Y } _ { 2 } = 203.7 , s _ { 2 } = 39.2$

A) $( - 29.0 , - 0.2 )$
B) $( - 1.5,30.7 )$
C) $( - 30.7,1.5 )$
D) $( - 26.8 , - 2.4 )$
E) $( - 1.3,30.5 )$