Use the Rank Correlation Coefficient to Test for a Correlation

question 98

Essay

Use the rank correlation coefficient to test for a correlation between the two variables. A
placement test is required for students desiring to take a finite mathematics course at a
university. The instructor of the course studies the relationship between students' placement
test score and final course score. A random sample of eight students yields the following data. $\begin{array}{cc}\underline {\text { Placement Score } } & \underline { \text { Final Course Score }} \\38 & 63 \\90 & 41 \\95 & 54 \\51 & 32 \\86 & 93 \\74 & 60 \\60 & 61 \\57 & 89\end{array}$ Compute the rank correlation coefficient, rs, of the data and test the claim of correlation
between placement score and final course score. Use a significance level of 0.05.

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Definitions:

Quintiles

Statistical values that divide a set of data into five equal parts, so that each part represents 1/5th of the sampled population.

Percentage Shares

Represent the portions or fractions, expressed as a percentage, of a whole divided among entities or allocated for specific purposes.

Poverty Line

A calculated income level used as a threshold to determine the minimum amount of income a family or individual needs to afford basic living expenses.

Poverty Rate

The percentage of the population that lives below the poverty line, indicating the level of economic deprivation in a community.