Use a Kruskal-Wallis Test to Test the Claim That the Samples

question 80

Essay

Use a Kruskal-Wallis test to test the claim that the samples come from populations with equal
medians. Listed below are grade averages for randomly selected students with three different
categories of high-school background. At the 0.05 level of significance, test the claim that the
three groups have the same median grade average. $$\begin{array}{l}\text { HIGH SCHOOL RECORD }\\\begin{array} { c c c } \text { Good } & \text { Fair } & \text { Poor } \\\hline 3.21 & 2.87 & 2.01 \\3.65 & 3.05 & 2.31 \\1.00 & 2.00 & 2.98 \\3.12 & 0.00 & 0.50 \\2.75 & 1.98 & 2.36\end{array}\end{array}$$

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Definitions:

Normally Distributed

A type of continuous probability distribution for a real-valued random variable whose graph forms the shape of a bell curve, often associated with the standard deviations and mean in data analysis.

Residuals

Differences between observed values and the values predicted by a model, showing the extent of deviation from a fit line.

Test Statistic F

The ratio of two variances that follows an F-distribution, used in statistical methods like ANOVA to determine the significance of group differences.

Degrees of Freedom

The number of independent values or quantities that can be assigned to a statistical distribution without violating any constraints.