A Statistics Course at a Large University Is Taught in Each

question 48

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. $$\begin{array}{l}\begin{array} { | c | c | c | c | c | } \hline { \text { Sample of semester } 1 \text { final marks } } \\\hline 65 & 45 & 53 & 76 & 53 \\\hline 85 & 55 & 63 & 85 & 77 \\\hline 45 & 57 & 55 & 60 & 83 \\\hline 96 & 83 & 55 & 52 & 67 \\\hline 82 & 64 & 62 & 88 & 71 \\\hline\end{array}&\begin{array} { | c | c | c | c | c | } \hline { \text { Sample of semester } 2 \text { final marks } } \\\hline 45 & 40 & 53 & 58 & 75 \\\hline 46 & 82 & 54 & 75 & 59 \\\hline 45 & 54 & 87 & 77 & 63 \\\hline 81 & 60 & 56 & 53 & 65 \\\hline 52 & 65 & 60 & 65 & 54 \\\hline\end{array}\end{array}$$ $$\begin{array}{l}\begin{array} { | l | c | } \hline { \text { Semester } 1 } \\\hline \text { Mean } & 65.48 \\\hline \text { Stan dard Error } & 2.679 \\\hline \text { Median } & 63 \\\hline \text { Mode } & 55 \\\hline \text { Standard Deviation } & 13.395 \\\hline \text { Sample Variance } & 179.43 \\\hline \text { Range } & 43 \\\hline \text { Minimum } & 45 \\\hline \text { Maximum } & 88 \\\hline \text { Sum } & 1637 \\\hline \text { Count } & 25 \\\hline\end{array}&\begin{array} { | l | c | } \hline { \text { Semester 2 } } \\\hline \text { Mean } & 60.96 \\\hline \text { Standard Error } & 2.5136 \\\hline \text { Median } & 59 \\\hline \text { Mode } & 54 \\\hline \text { Standard Deviation } & 12.568 \\\hline \text { Sample Variance } & 157.96 \\\hline \text { Range } & 47 \\\hline \text { Minimum } & 40 \\\hline \text { Maximum } & 87 \\\hline \text { Sum } & 1524 \\\hline \text { Count } & 25 \\\hline\end{array}\end{array}$$ There is a rumor going around the university that students with a higher IQ are enrolled in the semester 1 statistics course because they tend to be students enrolled in the degree with the higher entrance score for university. Can it be concluded at the 5% significance level that semester 1 students have a higher average final mark than semester 2 students? Assume that the population variances are unknown and equal.

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Definitions:

Social Learning Theory

A theory that suggests people learn new behaviors through observation, imitation, and modeling from others.

Behavioural Stage Model

A theoretical framework that describes the various phases individuals go through when changing their behavior.

Aggressive Behaviour

Actions or attitudes that are forceful, hostile, or attacking, often with the intent to dominate or intimidate.

Evolutionary Social Psychology

A branch of psychology that examines the influence of evolutionary processes on social behaviors and attitudes.