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Unformatted text preview: MATH 221 Statistics for Decision - Making Lecture Notes Week 6 Confidence Intervals Student Name We shall now examine confidence intervals and their role in the field of inferential statistics. Recall that Inferential Statistics is that branch of statistics that uses sample statistics to formulate inferences about population parameters. The key distinction between descriptive statistics and inferential statistics is that sample data can be used to form a meaningful estimate of the population from which the sample was drawn. Here are some key definitions to review. Population A population is considered as a complete set of measurements. Sample A sample is a subset of measurements taken from a population. Random Sample A random sample is a sample collected from the data in a random fashion. Often sampling means selection in an unbiased manner. Parameter A parameter is a numeric descriptive measure taken from a population. Statistic A statistic is a numeric descriptive measure taken from a sample. Point Estimate A point estimate is a single value used to estimate a population parameter. The sample mean is the best point estimate of the population mean. Example 1 Consider the data below which represents a random sample of railway prices ( in dollars ) for a two - way ticket from Detroit to Chicago. Copyright 2010 by P.E.P. 1 MATH 221 Statistics for Decision - Making Lecture Notes Week 6 Confidence Intervals Student Name Find a point estimate for the population mean. 99 100 102 105 95 98 120 100 99 94 Solution The point estimate for the price of all two - way tickets from Detroit to Chicago is the mean value of the above data or ( 99 + 100 + 102 + 105 + 95 + 98 + 120 + 100 + 99 + 94 ) / 10 = 101.20 For the subject of confidence intervals, we create intervals where an estimate can be found and examine the probability ( level of confidence ) of locating the estimate within the interval....
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