At a certain university, an English proficiency test must be passed before undergraduates can receive their degrees. Some students have been known to take the test twice before passing it. A random sample of 25 such students was taken, and the number of "comma errors" was counted on the first and second tests. The average difference on the two tests was a decrease of 2.4 errors. The standard deviation was 6.0.
a. If a college administrator wants to test to show that there was no improvement, what are the null and alternative hypotheses?
b. Perform the test.