ABSTRACT
In Chapter 5 we described how the standardised normal distribution is used when deciding if an observation could have been drawn from a given population with a known mean and standard deviation. In this chapter we will do something similar, but, instead of applying the process of hypothesis testing to individual observations, the process will be applied to sample means. For example, imagine we know that the population distribution of scores in a standardised test measuring reading speed is normal with µ = 200 words per minute and σ = 30. Moreover, imagine that a random sample of 36 people are given a crash course on how to read fast and that at the end of the course they read, on average 218 words per minute in the reading speed test. If we want to know whether the course was effective or not, we need to know how likely it is that our sample, with a mean of 218, is drawn from a population whose scores in the reading speed test are distributed as indicated above. If this probability is very low, then it is concluded that the sample was not drawn from a population with µ = 200 (i.e., that the reading course was effective). In this chapter we will give a detailed explanation of how to use the standardised normal distribution to answer questions of this type.
