A Statistics Course at a Large University Is Taught in Each

question 18

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. 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:

Normally Distributed

Describes a statistical distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence.

Mean

The average value of a set of numbers, indicating the central point of a data distribution.

Standard Normal

A normal distribution with a mean of zero and a standard deviation of one, used as the basis for z-scores in statistics.

Standard Deviation

A metric that calculates how much a dataset's values spread out or diverge from their average.