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

question 156

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.
-A coach uses a new technique in training middle distance runners. The times for 8 different athletes to run 800
meters before and after this training are shown below. $$\begin{array} { r | c c c c c c c c } \text { Athlete } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } & \text { H } \\\hline \text { Time before training (seconds) } & 112.7 & 115.2 & 109.2 & 117.2 & 113.9 & 118.7 & 115.2 & 110.4 \\\hline \text { Time after training (seconds) } & 113.3 & 113.9 & 106.8 & 118 & 112.1 & 118.8 & 111.6 & 106.5\end{array}$$ Using a 0.05 level of significance, test the claim that the training helps to improve the athletes' times for the 800
meters.

Understand the principle of duty of care and foreseeability in negligence cases.

Analyze the liability in cases of accidents involving animals.

Examine premises liability and the responsibilities of property owners towards invitees and trespassers.

Comprehend the concept of product liability and the duty of manufacturers towards consumers.

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Definitions:

Complex System

A system composed of interconnected parts that as a whole exhibit one or more properties (behavior among the parts) that are not obvious from the properties of the individual parts.

Meaning

The significance, definition, or purpose of something; what is intended to be expressed or indicated.

Organizations

Groups or entities that are structured and managed to meet a particular objective or set of objectives.

Goal Orientation

Refers to an individual's or organization's focus on setting and achieving specific objectives.