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:

Cognitive Perspective

An approach in psychology that emphasizes the study of how people think, perceive, remember, and learn, focusing on the processes involved in cognitive functions.

Anorexia Nervosa

An eating disorder characterized by an obsessive fear of gaining weight, which leads to a refusal to maintain a healthy body weight and a distorted body self-perception.

Bulimia Nervosa

An eating disorder marked by episodes of excessive eating followed by inappropriate methods of weight control, such as vomiting or excessive exercise.

Behavioral Therapist

A mental health professional who uses techniques based on learning theories to help patients modify maladaptive behaviors.