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:

Invincibility Fable

A cognitive bias often found in adolescents, believing themselves to be immune to common dangers.

Distribution

In statistics, the way in which data points are spread out across the scale of measurement.

Percentiles

Scores that indicate the percentage of scores in a distribution that a particular score is above or below.

Scores

Numerical representations of performance or achievement in educational settings, standardized tests, or other assessments.