# chp7 - CHAPTER 7...

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1 CHAPTER 7 Homework:5,7,9,11,17,22,23,25,29,33,37,41,45,51, 59,65,77,79 <Example 7.1>: The U.S. Bureau of Census publishes annual price figures for new mobile homes in Construction Reports. The information is obtained from sampling, not from a census. Suppose a random sample of 40 new mobile homes yields the prices shown in Table 7.1. Data are in thousands of dollars, rounded to the nearest hundred.

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2 Table 7.1 8.4 9.9 13.9 13.9 14.1 15.8 16.6 16.8 17.0 17.6 18.8 20.0 21.4 22.1 22.4 22.8 22.8 24.0 24.4 24.7 24.8 26.2 26.4 26.7 26.8 27.0 28.4 29.3 29.3 29.5 30.6 31.1 31.4 31.9 32.2 32.4 33.0 33.5 35.1 37.2 (a) Find the sample mean and sample standard deviation. (b) Find a point estimator for the population mean and a point estimator for the population standard deviation.
3 Out put 7. 01: Pr i ces of Mobi l e Homes SAS summar y st at i st i cs Anal ysi s Var i abl e : PRI CE N Mean St d Dev M i ni mum Maxi mum - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 40 24. 26 7. 20 8. 40 37. 20 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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4 10 15 20 25 30 35 Figure 7.1 Prices of Mobil Homes
5 <DISCUSSION>: (1) Point estimators do not provide any information of the reliability for itself. An interval estimator can provide the reliability information. Therefore, we want to construct an interval estimator of the population mean. (2) Usually, we need to have several reasonable assumptions about the population before we can actually construct the interval estimator.

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6 Interval Estimator An interval estimator is a rule that tells us how to use sample data to form an interval estimator of the population parameters. Confidence Coefficient: The confidence coefficient of an interval estimator is the probability that this interval estimator encloses the population parameter. Confidence Level: The confidence level is the confidence coefficient expressed as a percentage.
7 Sec 7.1: Large sample interval estimation of the population mean (a) Is the sample representative? We need to make sure that the sample is randomly selected from the population. This is one of the most basic principles of statistical inference.

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8 (b) Check the sample size If the sample size is greater than 30, you can use the large sample procedure because that: (i) the central limit theorem ensures at least approximate normality of the distribution of the sample mean and (ii) the law of large number ensures that the sample standard deviation provides a good estimator of the population standard deviation.
9 (c) Find the sample mean and standard error of the sample mean . S S n x = X

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(d) Find z α /2 , where α is equal to one minus confidence coefficient. The
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## This note was uploaded on 08/30/2011 for the course STA 2023 taught by Professor Bagwhandee during the Fall '07 term at University of Central Florida.

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chp7 - CHAPTER 7...

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