MSci_609_Estimation_with_Confidence_Inte

MSci_609_Estimation_with_Confidence_Inte - 1 ESTIMATION...

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2/5/2011 1 ESTIMATION WITH CONFIDENCE INTERVALS INSTRUCTOR: AMER OBEIDI 1 Statistica 2 Statistical Methods Inferential Statistics Descriptive Statistics Estimation Hypothesis Testing

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2/5/2011 2 Population Random Sample 3 Mean, , is unknown Sample Mean X = 50 I am 95% confident that is between 40 & 60. Target parameter Point estimate Et i t P lt i ith S l 4 Estimate Population Parameter. .. with Sample Statistic ^ Proportion pp Mean  x Differences 1 - 2 x 1 - x 2 Variance 2 s 2
2/5/2011 3 Statistical Methods 5 Hypothesis Inferential Statistics Descriptive Statistics Estimation Testing Interval Estimation Point Estimation 1. Provides a single value. Based on observations from one sampl 6 Based on observations from one sample 2. Gives no information about how close the value is to the unknown population parameter (i.e., no information about the reliability of estimate). 3. Example: Sample mean x = 3 is point estimate of unknown population mean

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2/5/2011 4 1. Provides a range of values Bd b t i f l 7 Based on observations from one sample 2. Gives information about closeness to unknown population parameter Stated in terms of probability Knowing exact closeness requires knowing unknown population parameter 3. Example: Unknown population mean lies between 50 and 70 with 95% confidence Sample statistic (point estimate) Confidence interval 8 Lower confidence limit Upper confidence limit A probability that the population parameter falls somewhere within the interval.
2/5/2011 5 The U.S. Census Bureau publishes annual price figures for new mobile homes in Manufacturing 9 Housing Statistics . The figures are obtained from sampling, not from a Census. A simple random sample of 36 new mobile homes yield the prices, in thousands of dollars, shown in the following table. Use this data to estimate the population mean price, μ , of all new mobile homes. 63.8 64.4 55.2 52.9 59.9 58.2 51.6 68.9 58.6 63.1 69.4 59.7 53.7 62.7 57.7 51.5 45.3 68.9 45.9 52.5 67.2 55.1 60.3 60.0 51.9 47.3 49.7 52.0 72.7 72.8 56.6 70.5 53.9 66.4 59.8 73.9 The sample mean price, is used to estimate population mean price, μ, of all new mobile homes. 10 Hence the estimated mean price of all mobile homes is approximately equal to \$59.28 k. Hence, the sample 2134.0 59.28 36 i x x n  mean price is a point estimate of μ . Still we need information about how this point estimate is reliable in telling us about the population parameter.

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2/5/2011 6 Assume that the standard deviation for the population is given, and it is \$7.2 thousands.
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This note was uploaded on 01/12/2012 for the course MSCI 609 taught by Professor Almehdawe,eman during the Fall '10 term at Waterloo.

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MSci_609_Estimation_with_Confidence_Inte - 1 ESTIMATION...

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