Chapter 5 - CHAPTER 5 INFERENCES ABOUT ONE POPULATION...

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CHAPTER 5: INFERENCES ABOUT ONE POPULATION CENTRAL VALUE 5.1 INTRODUCTION The objective of statistics is to make inferences about a population based on information contained in a sample. Populations are characterized by numerical descriptive measures called parameters . Typical population parameters are the population mean μ , the population median M , the population standard deviation σ , and a population proportion π . Most inferential problems can be formulated as an inference about one or more parameters of a population. For example, a study is conducted by the Texas Education Agency to assess the reading ability of children in the primary grades. The population consists of the scores on a standard reading test of all children in the primary grades in Texas. We are interested in estimating the value of the population mean score μ and the proportion π of scores below a standard, which designates that a student needs remedial assistance. ESTIMATION AND HYPOTHESIS TESTING Methods for making inferences about parameters fall into one of two categories. Either we will estimate (or predict ) the value of the population parameter of interest or we will test a hypothesis about the value of the parameter. These two methods of statistical inference – estimation and hypothesis testing – involve different procedures, and, more importantly, they answer two different questions about the parameter. In estimating a population parameter, we are answering the question, “ What is the value of the population parameter? ” In testing a hypothesis , we are answering the question, “ Is the parameter value equal to this specific value? Consider a study in which an instructor wishes to examine the effectiveness of a newly developed one-month-long computer-based statistics instruction in reducing hand- computation anxiety levels of anxious students in his statistics class. The instructor uses scores his students obtained in a previous college calculus course to identify a group of 30 students who are anxious about carrying out hand computations. After the students are taught some key statistics concepts and applications thru the computer-based teaching approach, each one’s anxiety level is measured on a rating scale (ranging from 0 to 10 ) immediately before he or she takes the first lesson and then at the end of the one-month-long computer-based statistics instruction. The sample data collected from these 30 students can be used to make inferences about the population from which the sample was drawn either by estimation or by a statistical test: Dr. LOHAKA – QBA 2302 Chap. 5: INFERENCES ABOUT ONE POPULATION VALUE Page 183
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Estimation : Information from the sample can be used to estimate (or predict) the mean decrease in anxiety ratings for the set of all hand-computation anxious students who may conceivably be taught statistics by the lately designed software.
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