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

question 62

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

---

Definitions:

Sigmund Freud

An Austrian neurologist and the founder of psychoanalysis, a method for treating psychopathology through dialogue between a patient and a psychoanalyst.

Erik Erikson

A developmental psychologist known for his theory on the psychosocial development of humans, emphasizing the impact of society and culture.

Lawrence Kohlberg

An American psychologist best known for his theory of stages of moral development.

Conservation

The protection, preservation, management, or restoration of natural environments and the ecological communities that inhabit them.