Each year, U.S. News and World Report publishes rankings of colleges based on statistics such as admis¬sion rates, graduation rates, class size, faculty-student ratio, faculty salaries, and peer rat¬ings of administrators. Economists Christopher Avery, Mark Glickman, Caroline Minter Hoxby, and Andrew Metrick took an alternative approach of analyzing the college choices of 3240 high-achieving school seniors. They examined the colleges that offered admission along with the colleges that the students chose to attend. The table below lists rankings for a small sample of colleges. Find the value of the rank correlation coefficient and use it to determine whether there is a correlation between the student rankings and the rankings of the magazine.
Use a 0.05 significance level with the indicated test. If no particular test is specified, use the appropriate nonparametric test from this chapter.
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