Random Behavior of Means notes (1)

# Random Behavior of Means notes (1) - Random Behavior of...

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Sections 3.6 and 3.7 Page 1 Random Behavior of Means Goals h We want to estimate characteristics about a population using a sample h We can Estimate Population Characteristics with Relatively Small Samples h Step one is to select a random sample from the population of interest. Random Sample h A random sample of size n is one drawn such that all samples of size n have the same chance of being chosen. h A random sample is one in which all the observations are statistically independent and follow exactly the same distribution. h We say that the members of the sample are independent and identically distributed (iid). h We will always assume that data comes from a random sample.

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Sections 3.6 and 3.7 Page 2 Examples: Statistic Parameter Describes a sample Describes a population Always known Usually unknown Changes with repeated sampling Is fixed Sampling h Upon repeated sampling of the same population, the value of a statistic changes b variable. h While we don’t know what the next value will be, we do know the overall pattern over many, many samplings b random. h The distribution of possible values of a statistic for repeated samples of the same size from a population is called the sampling distribution of the statistic. Sampling Distribution of If a random sample of size n is taken from a normal population having mean and variance then is a random variable which is also normally distributed with mean and variance
Sections 3.6 and 3.7 Page 3 Sampling Distribution of Light Bulbs h The life of a light bulb is normally distributed with a mean of 2000 hours and standard deviation

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Random Behavior of Means notes (1) - Random Behavior of...

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