A Statistics Course at a Large University Is Taught in Each

question 87

Essay

A statistics course at a large university is taught in each semester. A student has noticed that the students in semester 1 and semester 2 are enrolled in different degrees. To investigate, the student takes a random sample of 25 students from semester 1 and 25 students from semester 2 and records their final marks (%) provided in the table below. Excel was used to generate descriptive statistics on each sample.
Assume that student final marks are normally distributed in each semester. $$\begin{array}{l}\begin{array} { | c | c | c | c | c | } \hline { \text { Sample of semester } 1 \text { final marks } } \\\hline 65 & 45 & 53 & 76 & 53 \\\hline 85 & 55 & 63 & 85 & 77 \\\hline 45 & 57 & 55 & 60 & 83 \\\hline 96 & 83 & 55 & 52 & 67 \\\hline 82 & 64 & 62 & 88 & 71 \\\hline\end{array}&\begin{array} { | c | c | c | c | c | } \hline { \text { Sample of semester } 2 \text { final marks } } \\\hline 45 & 40 & 53 & 58 & 75 \\\hline 46 & 82 & 54 & 75 & 59 \\\hline 45 & 54 & 87 & 77 & 63 \\\hline 81 & 60 & 56 & 53 & 65 \\\hline 52 & 65 & 60 & 65 & 54 \\\hline\end{array}\end{array}$$ $$\begin{array}{l}\begin{array} { | l | c | } \hline { \text { Semester } 1 } \\\hline \text { Mean } & 65.48 \\\hline \text { Stan dard Error } & 2.679 \\\hline \text { Median } & 63 \\\hline \text { Mode } & 55 \\\hline \text { Standard Deviation } & 13.395 \\\hline \text { Sample Variance } & 179.43 \\\hline \text { Range } & 43 \\\hline \text { Minimum } & 45 \\\hline \text { Maximum } & 88 \\\hline \text { Sum } & 1637 \\\hline \text { Count } & 25 \\\hline\end{array}&\begin{array} { | l | c | } \hline { \text { Semester 2 } } \\\hline \text { Mean } & 60.96 \\\hline \text { Standard Error } & 2.5136 \\\hline \text { Median } & 59 \\\hline \text { Mode } & 54 \\\hline \text { Standard Deviation } & 12.568 \\\hline \text { Sample Variance } & 157.96 \\\hline \text { Range } & 47 \\\hline \text { Minimum } & 40 \\\hline \text { Maximum } & 87 \\\hline \text { Sum } & 1524 \\\hline \text { Count } & 25 \\\hline\end{array}\end{array}$$ Estimate and interpret a 95% confidence interval for the population average final mark for semester 1 students.

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Definitions:

Self-reliance

The reliance on one's own powers and resources rather than those of others.

Aggressiveness

A behavior characterized by hostility or attack, which can be physical or verbal, driven by intentions to dominate or harm others.

Competition

The rivalry between entities for resources, recognition, or victory in activities ranging from sports to business to natural selection.

Margaret Mead

An American cultural anthropologist who played a major role in developing the field of anthropology and understanding of cultural patterns.