Refer to the Human Factors study of the performance of a computerized speech recognizer, Exercise 12.26. Recall that the researchers built a complete second-order model for task completion time (y) as a function of accuracy (x₁) and vocabulary (x₂).

a. Give the null hypothesis for testing whether the quadratic terms in the model are useful predictors of y.

b. The test, part a, resulted in a p-value of less than .01. Interpret this result.

Data from Exercise 12.26

A study reported in Human Factors (Apr. 1990) investigated the effects of recognizer accuracy and vocabulary size on the performance of a computerized speech recognition device. Accuracy (x₁) of the device, measured as the percentage of correctly recognized spoken utterances, was set at three levels: 90%, 95%, and 99%. Vocabulary size (x₂), measured as the percentage of words needed for the task, was also set at three levels: 75%, 87.5%, and 100%. The dependent variable of primary interest was task completion time (y, in minutes), measured from when a user of the recognition device spoke the first input until the recognizer displayed the last spoken word of the task. Data collected for n = 162 trials were used to fit a complete second-order model for task completion time (y), as a function of the quantitative independent variables accuracy (x₁) and vocabulary (x₂). The coefficient of determination for the model was R² = .75.