show the math for $8\mathrm{.}9,$ DO NOT DO CODE IN R

$8\mathrm{.}9$

The data set fosdata:scows$\_$small gives the change in shoulder temperature of cows standing in the

heat.

a$.$ Give the $95\%$ confidence interval for the shoulder temperature change after spraying with the tk$\_(-)12$

nozzle.

b$.$ Give the $95\%$ confidence interval for the shoulder temperature change after no spraying $($

c$.$ Which of the two intervals is wider?

d$.$ What is the standard deviation of temperature change for the

condition? For the

condition?

e$.$ How are your answers to parts $($c$)$ and $($d$)$ related?