Construct a Confidence Interval For $\mu _ { \mathrm { d } }$

Essay

Construct a confidence interval for $\mu _ { \mathrm { d } }$ , the mean of the differences d for the population of paired data. Assume that the
population of paired differences is normally distributed.
-The table below shows the weights of seven subjects before and after following a particular diet for two months. $$\begin{array} { l | c c c c c c c } \text { Subject } & \mathrm { A } & \mathrm { B } & \mathrm { C } & \mathrm { D } & \mathrm { E } & \mathrm { F } & \mathrm { G } \\\hline \text { Before } & 178 & 167 & 194 & 154 & 174 & 156 & 194 \\\hline \text { After } & 171 & 158 & 192 & 159 & 160 & 158 & 182\end{array}$$ Using a 0.01 level of significance, test the claim that the diet is effective in reducing weight.