1. An advertisement for a word-processing class claims that students who

class will, on average, be able to type 60 wpm

(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 an answer, using a significance level of .05.

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)?'

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?

2. Consider the one-sided situation in problem 1: An advertisement for a word-processing class claims that students who complete the class will, on average, be able to type 60 (wpm) with a standard deviation of 6 wpm. We're concerned that students aren't performing as well as advertised. At the end of the class we test 49 students and conduct a one- sided hypothesis test at the .05 level of significance. This means that the hypothesis will be rejected if the mean wpm is less than 58.6. Suppose, in reality, the true mean for graduates is 58 wpm with a standard deviation of 5 wpm.

A. What's the probability of a type II error?

B. What's the power of the test if the true population mean is 58 wpm? Draw

a diagram of the sampling distribution for the sample mean, showing the

area that represents the power of the test and the area that represents the

probability of a type II error.