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Over 2000 photomultiplier tubes have been selected as the readout device of the upgrade CDF Endplug calorimeter, a scintillator tile sampling calorimeter with wave-shifter fiber readout. The specifications were set on various properties of the tubes for the electromagnetic and hadronic compartments and a series of rigorous tests were made on 2216 Hamamatsu R4125, 10-stage 19 mm diameter tubes with green-extended bialkali photocathode. On all of the test items, the distributions of the data were well clustered with minor tails, and the original specifications based on a small ensemble were well suited for rejecting the tails of the distributions. After rejecting 5.4% of the total, 960 tubes for electromagnetic and 864 tubes for hadronic compartments were allocated to projective towers based on their linear dynamic ranges. Tubes with greater linear ranges were assigned to larger pseudo-rapidity channels where greater single-tower energy deposits were expected. This paper describes how we selected the phototubes for our calorimeter and presents the results of the study we made. [Copyright &y& Elsevier]