A Statistics Professor at an All-Womenʹs College Determined That the Standard

question 136

Essay

A statistics professor at an all-womenʹs college determined that the standard deviation of womenʹs heights is
2.5 inches. The professor then randomly selected 41 male students from a nearby all-male college and found
the standard deviation to be 2.9 inches. Test the professorʹs claim that the standard deviation of male heights is
greater than 2.5 inches. Use $\alpha$ = 0.01.

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Definitions:

Representative of the Population

A sample group or individual characteristics that accurately reflect the larger population from which they're drawn.

Positive Correlation

A relationship between two variables in which both variables move in tandem, meaning as one variable increases, the other one also increases.

Two Factors

A concept or principle that involves two different elements or conditions contributing to a particular outcome or situation.

Random Sampling

A method of selecting a sample from a population where each member has an equal chance of being chosen, ensuring the results are representative.