A Statistics Course at a Large University Is Taught in Each

question 12

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. $$\begin{array}{l}\begin{array} { | c | c | c | c | c | } \hline { \text { Sample of semester } 1 \text { fin al marks } } \\\hline 69 & 45 & 53 & 76 & 53 \\\hline 89 & 59 & 63 & 89 & 77 \\\hline 49 & 57 & 59 & 60 & 83 \\\hline 96 & 83 & 59 & 92 & 67 \\\hline 82 & 64 & 62 & 88 & 71 \\\hline\end{array}&\begin{array} { | c | c | c | c | c | } \hline { \text { Sample of semester } 2 \text { fin al marks } } \\\hline 49 & 40 & 93 & 58 & 79 \\\hline 46 & 82 & 54 & 79 & 59 \\\hline 45 & 54 & 87 & 77 & 63 \\\hline 81 & 60 & 96 & 53 & 69 \\\hline 92 & 69 & 60 & 69 & 54 \\\hline\end{array}\end{array}$$ $$\begin{array}{l}\begin{array} { | l | c | } \hline { \text { Semester } 1 } \\\hline \text { Mean } & 65.48 \\\hline \text { Stan dard Error } & 2.679 \\\hline \text { Median } & 63 \\\hline \text { Mode } & 55 \\\hline \text { Standard Deviation } & 13.395 \\\hline \text { Sample Variance } & 179.43 \\\hline \text { Range } & 43 \\\hline \text { Minimum } & 45 \\\hline \text { Maximum } & 88 \\\hline \text { Sum } & 1637 \\\hline \text { Count } & 25 \\\hline\end{array}&\begin{array} { | l | c | } \hline { \text { Semester 2 } } \\\hline \text { Mean } & 60.96 \\\hline \text { Standard Error } & 2.5136 \\\hline \text { Median } & 59 \\\hline \text { Mode } & 54 \\\hline \text { Standard Deviation } & 12.568 \\\hline \text { Sample Variance } & 157.96 \\\hline \text { Range } & 47 \\\hline \text { Minimum } & 40 \\\hline \text { Maximum } & 87 \\\hline \text { Sum } & 1524 \\\hline \text { Count } & 25 \\\hline\end{array}\end{array}$$ Can we conclude at the 5% significance level that the variance of semester 2 student's final marks is greater than 150?

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Definitions:

Extraverts

Individuals characterized by their outgoing, sociable, and energetic behavior, often drawing energy from interacting with others.

Introverts

Individuals who tend to be more inward turning, focusing on internal thoughts, feelings, and moods rather than seeking out external stimulation.

Organizational Citizenship Behaviours

Voluntary actions of employees that contribute to the organization but are not part of their formal job requirements.

Big Five

Refers to the five broad personality traits used in psychology to describe human personality: openness, conscientiousness, extraversion, agreeableness, and neuroticism.