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:

Consolidated Cash Account

A single cash account that combines the cash balances of a parent company and its subsidiaries to reflect total available cash.

Subsidiary Entities

Companies that are controlled by another company (parent company) through ownership of more than half of the voting power or through other means of control.

Consolidated Share Capital

The total amount of a parent company's share capital together with its subsidiaries, reported as one figure in the consolidated financial statements.

Issued Share Capital

Refers to the total value of a company's shares that have been sold to investors and are currently outstanding.