The ability to recognize an auditory "signal" presented against a background of auditory "noise" is important to a particular job. A company tests for this ability by presenting 100 trials of auditory noise. During each trial the subject must state whether or not a signal has also been presented. A training program has been used to try to improve performance in this test. A random sample of 50 persons, who have had the training program, are administered the auditory test and they make an average of 32.2 errors.
a) The company's records indicated that in the past the mean number of errors has been 32.6 with a variance of 2.25. Does the training program improve test performance? (Use alpha less than or equal to 0.05)
b) With alpha less than or equal to 0.02, form a confidence interval to estimate the mean number of errors that would be made by all subjects who undergo the training program. [31.71 to 32.69]