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:

Demand Curve

A graphical representation showing the relationship between the price of a good and the quantity demanded by consumers.

Price Elasticity

A measure of how much the quantity demanded of a good responds to a change in the price of that good, indicating the sensitivity of consumers to price changes.

Demand Curve

A graph showing the relationship between the price of a good or service and the quantity demanded for it at those prices, typically downward sloping.

Law of Diminishing

A principle that states the incremental utility or benefit gained from consuming additional units of a good or service tends to decrease with each additional unit consumed.