Two Students,Mary and Joanna,are in a Statistics Class Working Hard

question 50

Essay

Two students,Mary and Joanna,are in a statistics class working hard on the consistency of their performance in the weekly class tests.In particular,they are hoping to bring down the variance of their test scores.Their professor believes that the students are not equally consistent in their tests.Over a 12-week period,the test scores of these two students are shown below.Assume that the two samples are drawn independently from normally distributed populations. a.Develop the hypotheses to test whether the two students differ in consistency.
b.Use the critical value approach to test the professor's claim at α = 0.05.

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Definitions:

Null Hypothesis

A statistical hypothesis that assumes no significant difference or effect exists between certain datasets or parameters.

Alternative Hypothesis

The hypothesis that there is a significant difference between specified populations, any observed difference being due to sampling or experimental error.

Confidence Interval

A range of values that is likely to contain a population parameter with a certain level of confidence.

Null Hypothesis

A default hypothesis that there is no effect or no difference, and the observed outcomes are due to chance; it is the hypothesis tested for possible rejection in statistical analysis.