Battery
a New Brand of Battery for Use in Calculators

Battery
A new brand of battery for use in calculators and cameras is said to last significantly longer than another brand.A camera manufacturer is to test this brand (Y)with brand (X)to see if brand Y has a longer life.If brand Y does last longer,the camera manufacturer will equip their new cameras with them.If not,they will equip them with brand X that is less costly.Twenty cameras are equipped as follows: ten with brand Y batteries and ten with brand X batteries and the life of the batteries measured.Is brand Y superior (does it last longer)to brand X? To answer this question,the camera manufacturer uses a 0.01 significance level and knows that the populations are normally distributed with equal variances.Sample data are: $$\begin{array} { | c | c | } \hline \text { Brand } \boldsymbol { X } & \text { Brand } \boldsymbol { Y } \\\hline n _ { 1 } = 10 & n _ { 2 } = 10 \\\bar { x } _ { 1 } = 500 \text { hours } & \bar { x } _ { 2 } = 650 \text { hours } \\s _ { 1 } ^ { 2 } = 400 & s _ { 2 } ^ { 2 } = 484 \\\hline\end{array}$$
-State the conclusion.