Two faculty members ranked 12 candidates for scholarships. Calculate the Spearman rank-correlation coefficient and test it for significance. Use a .02 level of significance. Candidate 1 2 3 4 5 6 7 8 9 10 11 12 Rank by Professor A 6 10 2 1 5 11 4 3 7 12 9 8 Rank by Professor B 5 11 6 3 4 12 2 1 7 10 8 9 The P-value for testing the significance of rank-correlation is The Spearman Rank Correlation Coefficient is
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| Candidate | Rank A | Rank B | d | d^2 | |-----------|--------|--------|----|-----| | 1 | 6 | 5 | 1 | 1 | | 2 | 10 | 11 | -1 | 1 | | 3 | 2 | 6 | -4 | 16 | | 4 | 1 | 3 | -2 | 4 | | 5 Show more…
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Perform these steps. a. Find the Spearman rank correlation coefficient. b. State the hypotheses. c. Find the critical value. Use $\alpha=0.05$. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Cyber School Enrollments Shown are the numbers of students enrolled in cyber school for five randomly selected school districts and the per-pupil costs for the cyber school education. At $\alpha=0.10$, is there a relationship between the two variables? How might this information be useful to school administrators? $$ \begin{array}{l|ccccc} \text { Number of students } & 10 & 6 & 17 & 8 & 11 \\ \hline \text { Per-pupil cost } & 7200 & 9393 & 7385 & 4500 & 8203 \end{array} $$
Nonparametric Statistics
The Spearman Rank Correlation Coefficient and the Runs Test
Perform these steps. a. Find the Spearman rank correlation coefficient. b. State the hypotheses. c. Find the critical value. Use $\alpha=0.05$. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Mathematics Achievement Test Scores The National Assessment of Educational Progress (U.S. Department of Education) tests mathematics, reading, and science achievement in grades 4 and 8 . A random sample of states is selected, and their mathematics achievement scores are noted for fourth- and eighth-graders. At $\alpha=0.05,$ can a linear relationship be concluded between the data? $$ \begin{array}{l|rrrrrrr} \text { Grade } \mathbf{4} & 90 & 84 & 80 & 87 & 88 & 77 & 79 \\ \hline \text { Grade } \mathbf{8} & 81 & 75 & 66 & 76 & 80 & 59 & 74 \end{array} $$
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