Construct a Confidence Interval for µD, the Mean of the Differences

question 96

Multiple Choice

Construct a confidence interval for µd, 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 9 different athletes to run 800 meters before and after this training are shown below. $\begin{array} { c | c c c c c c c c } \text{Athlete} & A&B&C&D&E&F&G&H&I\\\hline\text{ Time before} &115.2&120.9&108.0&112.4&107.5&119.1&121.3&110.8&122.3 \\\text{training (seconds) }\\\hline\text{ Time AFTER} &116.0&119.1&105.1&111.9&109.1&115.2&118.5&110.7&120.9\\\text{training (seconds) }\\\end{array}$
Construct a $99 \%$ confidence interval for the mean difference of the "before" minus "after" times.

• A) \(- 0.85 < \mu _ { \mathrm { d } } < 3.29\)
• B) \(- 0.76 < \mu _ { \mathrm { d } } < 3.20\)
• C) \(- 0.82 < \mu _ { \mathrm { d } } < 3.26\)
• D) \(- 0.54 < \mu _ { \text {d } } < 2.98\)

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Definitions:

Organization

A structured group of individuals working together to achieve common goals or objectives, often characterized by a set hierarchy or operating system.

Maslow

Abraham Maslow was an American psychologist best known for creating Maslow's hierarchy of needs, a theory of psychological health predicated on fulfilling innate human needs in priority, culminating in self-actualization.

Herzberg

Related to Frederick Herzberg's Motivation-Hygiene Theory, which suggests that job satisfaction and dissatisfaction stem from different factors.

McGregor

Refers to Douglas McGregor's Theory X and Theory Y, which describe two contrasting models of workforce motivation and management.