An advertisement for a word-processing class claims that students who complete the class will, on average, be able to type 60 words per minute (wpm) with a standard deviation of 6 wpm. at the end of the class, 49 students are tested and their mean score is 58.5 wpm.

a. is this evidence that the true mean is different from 60 wpm? give a complete answer, using a significance level of .05. (12 points)
b. suppose the person conducting the research had believed, before collecting data, that the graduates weren't as good as claimed. would this belief have changed the analysis you performed in part (a)? (12 points)
c. construct a 99% confidence interval for the true mean of the population. what conclusion can you draw from this interval, and do you have evidence to reject the claim that the average graduate can type 60 wpm? (6 points)