The Carnegie Classification of Institutes of Higher Education categorizes colleges and universities on the basis of their research and degree-granting activities. Universities that grant doctoral degrees are placed into one of three classifications: moderate research activity, higher research activity, or highest research activity. The Carnegie classifications for public and not-for-profit private doctoral degree-granting universities are summarized in the following table. 

Test the hypothesis that the population proportions of public universities are equal in each Carnegie classification category. Use a .05 level of significance. What is the p-value and what is your conclusion?

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Carnegie Classification Type of University Moderate Higher Research Activity Research Activity Highest Research Activity Public 38 76 81 Private 58 31 34