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:

Universal Screening

A systematic procedure applied to all individuals within a specific group to identify those at risk or displaying certain characteristics, without prior identification.

RTI Approach

Response to Intervention (RTI) is an educational strategy focused on early detection and support for students with learning and behavior needs.

Every Student Succeeds Act

A United States law signed in 2015 that aims to ensure public schools provide a quality education for all children, focusing on accountability, flexibility, and state-specific standards.

ELLs

English Language Learners; individuals who are learning English as a second language in addition to their native language.