A University Lecturer Claims That Students Who Attend Lecturers Score

question 21

Essay

A university lecturer claims that students who attend lecturers score a higher final mark in her course than students who watch the lecture recordings online. The lecturer takes a random sample of the final marks of 40 students who attended her university lectures and found their average mark was 65 with a standard deviation of 5. The lecturer takes a random sample of 30 university students who watched the lecture recordings online and found their average mark was 60 with a standard deviation of 8. Is there significant evidence to support this university lecturer's claim? Test at the 5% level of significance, assuming that the population variances are unequal.

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Definitions:

Confidence Interval

A range of values, derived from a data set, within which the true parameter value is estimated to lie with a certain level of confidence.

Expected Value

The weighted average of all possible values of a random variable, weighted by their respective probabilities.

Simple Linear Regression

A method of fitting a straight line through a set of data points to model a linear relationship between two variables.

Prediction Interval

An interval estimate of a real-valued observation based on a sample of data predicting where an individual measurement will fall.