Population and Means
Discussion Instructions Consider some test score (or other interval level measurement) that is important in your field of specialization. Consider that you have, in a database, the entire population of scores for people in a defined geographic area, and they are slightly skewed, but reasonably close to normal. Assume you randomly selected a sample of 75 scores, computed the mean of the sample, and then left the scores in the list to be selected again later. You then repeated this process 1000 times. In the end, you would have 1000 means for 1000 random samples. Explain three things you would be able to predict about the relationship between the population and the list of 1000 means. While you do not have to explicitly respond to the following statements and questions, in order to post intelligently to this discussion, you must understand the concepts they represent: How is a z score computed? What two known quantities of a sample must be available to compute it? Explain the relationship between a z score and a standard deviation. A sample of scores has a mean and standard deviation. What are the corresponding quantities in a sampling distribution? How does a sampling distribution compare to a distribution of scores? For a single population (a large set) of scores, how many sampling distributions exist (including the raw score distribution itself) that have sample sizes less than 64? For a given population, explain which of the two sampling distribution parameters change, and how it changes, as sample size increases.
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