In most statistical studies we do not have access to

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In most statistical studies, we do not have access to the entire population and can consider only data for a sample from that population. Our ultimate goal is to make conclusions about the larger population, based on only the sample data. Up until now, we have generally been assuming we have a representative sample from an infinite on- going process (e.g., dog identification of cancer sample, hospital transplant operations, candy manufacturing). We made some assumptions, like the process is not changing over time and that there is no tendency to select some types of outcomes more than others (e.g., getting the first 5 candies from the manufacturing process rather than throughout the day). In fact, a binomial process assumes you have repeat observations from the exact same process but with randomness in the actual outcome that occurs (sometimes the dog makes the correct identification, some time she does not). In this case, instead of sampling from an on-going process we are sampling from a finite population (the 268 words). In fact, we actually have access to the entire population. But what if we didn’t? We still need some way of convincing people that are sample is likely to be representative of the population. To do that, we will explore for a minute, using this population to see how samples behave where “random chance” arises from which observational units are selected to be in the sample, rather than from “random choices” made by the observational units. (b) Consider the sample you selected in (a). Suppose I wanted to focus on the lengths of the words in the sample (if the sample is truly representative, it shouldn’t matter what variable I end up recording). Record the ten lengths that you found. 1 2 3 4 5 6 7 8 9 10 Length (c) Identify the observational units and variable for this sample. Obs units: Variable: Type:
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Chance/Rossman, 2015 ISCAM III Investigation 1.12 96 (d) Do you think the words you selected are representative of the population of 268 words in this passage? How are you deciding? Definition: The term parameter , before considered the process probability, is also used to refer to a numerical characteristic of a population . We will continue to denote population parameters with Greek letters, for example S or P for a population proportion or population mean, respectively. A statistic continues to be the corresponding number but calculated from sample data. We denote the statistics for a sample proportion and a sample mean by and x , respectively. (e) Calculate the average length of the ten words in your sample. Is this number a parameter or a statistic? What symbol can we use to refer to it? Average: Parameter or statistic? Symbol: (f) The average length of all 268 words in this population is 4.29 letters. Is this number a parameter or a statistic? What symbol can we use to refer to it?
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