A Statistics Course at a Large University Is Taught in Each

question 61

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 90% confidence interval of the ratio of population variances of final student marks from semester 1 and semester 2.

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Definitions:

Sociological Imagination

The ability to see the relationship between individual experiences and larger social influences, coined by C. Wright Mills.

Spencer's Idea

Associated with Herbert Spencer, who applied evolutionary theory to sociology and philosophy, advocating that society evolves through survival of the fittest.

Symbolic Interactionism

An approach in sociology that emphasizes the role of symbols and language as core elements of all human interaction.

Fundamental Principles

Basic concepts or ideas that serve as the foundation for a system, theory, or belief.