Suppose It Desired to Compare Two Physical Education Training Programs

question 74

Essay

Suppose it desired to compare two physical education training programs for preadolescent girls. A total of 82 girls are randomly selected, with 41 assigned to each program. After three 6-week periods on the program, each girl is given a fitness test that yields a score between 0 and 100. The means and variances of the scores for the two groups are shown in the table. $$\begin{array}{l}\begin{array} { l | c | c | c } & n & \bar { x } & s ^ { 2 } \\\hline \text { Program 1 } & 41 & 78.5 & 201.7 \\\text { Program 2 } & 41 & 75.8 & 259.6\end{array}\\\\\text { Test to determine if the variances of the two programs differ. Use } \alpha = .05 \text {. }\end{array}$$

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Definitions:

Mean

The arithmetic average of a set of numbers, calculated by dividing the sum of the values by the number of values.

Probability

A measure of the likelihood that an event will occur, expressed as a number between 0 and 1.

Standard Deviations

A measure of the amount of variation or dispersion of a set of values from the mean.

Z Score

A statistical measurement that describes a value's relationship to the mean of a group of values, expressed in standard deviations.