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

question 5

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.

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Definitions:

Purely Competitive Industry

Characterized by many firms selling identical products, where no single firm can influence the market price, ensuring competition based on price.

Short-Run Costs

Costs that vary with the level of output in the short term, where some inputs are fixed.

Fertilizer

A substance, either chemical or organic, introduced to soil or land to improve its fertility and boost the growth of plants.

Purely Competitive Industry

Markets where many sellers are offering a homogeneous product, and no single seller can influence the price.