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

question 166

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 to train gymnasts. 7 gymnasts were randomly selected and their competition
scores were recorded before and after the training. The results are shown below. $$\begin{array} { c | c c c c c c c } \text { Subject } & \mathrm { A } & \mathrm { B } & \mathrm { C } & \mathrm { D } & \mathrm { E } & \mathrm { F } & \mathrm { G } \\\hline \text { Before } & 9.5 & 9.4 & 9.6 & 9.5 & 9.5 & 9.6 & 9.7 \\\hline \text { After } & 9.6 & 9.6 & 9.6 & 9.4 & 9.6 & 9.9 & 9.5\end{array}$$ Using a 0.01 level of significance, test the claim that the training technique is effective in raising the gymnasts'
scores.

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Definitions:

Hallucinogen

A substance that induces alterations in perception, thinking, and feeling, leading to hallucinations that are not real.

Stimulant

A substance that increases physiological or nervous activity in the body.

Cerebral Cortex

The outer layer of the brain involved in complex cognitive processes like reasoning, language, and consciousness.

Impaired Vision

A reduction or lack of visual capability resulting from conditions affecting the eyes or visual processing areas in the brain.