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Many developers of audio signal processing strategies rely on objective measures of quality for initial evaluations of algorithms. As such, objective measures should be robust, and they should be able to predict quality accurately regardless of the dataset or testing conditions. Kates and Arehart have developed the Hearing Aid Speech Quality Index (HASQI) to predict the effects of noise, nonlinear distortion, and linear filtering on speech quality for both normal-hearing and hearing-impaired listeners, and they report very high performance with their training and testing datasets [Kates, J. and Arehart, K., Audio Eng. Soc., 58(5), 363-381 (2010)]. In order to investigate the generalizability of HASQI, we test its ability to predict normal-hearing listeners' subjective quality ratings of a dataset on which it was not trained. This dataset is designed specifically to contain a wide range of distortions introduced by real-world noises which have been processed by some of the most common noise suppression algorithms in hearing aids. We show that HASQI achieves prediction performance comparable to the Perceptual Evaluation of Speech Quality (PESQ), the standard for objective measures of quality, as well as some of the other measures in the literature. Furthermore, we identify areas of weakness and show that training can improve quantitative prediction.