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

question 62

Essay

Construct a confidence interval for μd\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.
-Five students took a math test before and after tutoring. Their scores were as follows.  Subject  A  B  C  D  E  Before 7166677775 After 7575658087\begin{array} { | c | c c c c c | } \hline \text { Subject } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \\\hline \text { Before } & 71 & 66 & 67 & 77 & 75 \\\hline \text { After } & 75 & 75 & 65 & 80 & 87 \\\hline\end{array} Using a 0.01 level of significance, test the claim that the tutoring has an effect on the math scores.

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Definitions:

Autonomic

Relating to the autonomic nervous system, which controls involuntary bodily functions, including heart rate, digestion, and respiratory rate.

Meninges

The three protective membranes that cover the brain and spinal cord, including the dura mater, arachnoid mater, and pia mater.

Glia

Non-neuronal cells in the central nervous system that support, protect, and nourish neurons.

Ventricles

Hollow structures within the brain that produce and store cerebrospinal fluid, or chambers of the heart that pump blood.

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