Recording electrical activity of the brain is important in clinical problems as well as in neurophysiological research. To improve the signal-to-noise ratio (SNR) in the electrical activity, it is necessary to repeatedly stimulate subjects and average the responses— a procedure that assumes that single responses are homogeneous. A study was conducted to test the homogeneous signal theory (IEEE Engineering in Medicine and Biology Magazine, Mar. 1990). The null hypothesis is that the variance of the SNR readings of subjects equals the “expected” level under the homogeneous signal theory. For this study, the “expected” level was assumed to be .54. If the SNR variance exceeds this level, the researchers will conclude that the signals are nonhomogeneous.

a. Set up the null and alternative hypotheses for the researchers.

b. SNRs recorded for a sample of 41 normal children ranged from .03 to 3.0. Use this information to obtain an estimate of the sample standard deviation.

c. Use the estimate of s in part b to conduct the test of part a. Test using α = .10.