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7.1,7.2

# 7.1,7.2 - corresponding sample statistic due to the fact...

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Lecture 10 7.1- Sampling Error- The Need for Sampling Distributions 7.2- The Mean and Standard Deviation of the Sample Mean Population Parameter, Sample Statistics A population is the collection of all items under consideration while a sample is the part of the population about which information is collected. Descriptive measures for a population are called parameters while analogous descriptive measures for the sample are called statistics. The value of a population parameter is always a constant. The value of a sample statistic depends on the sample selected, hence a statistic is a random variable. The sample statistic follows a probability distribution, called sampling distribution. Sampling and Non-Sampling Errors In general, the population parameter is not equal to the corresponding sample statistic. The Sampling Error refers to the difference between the population parameter and the
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Unformatted text preview: corresponding sample statistic due to the fact information is collected only about a sample. The Non-Sampling Error refers to the difference between the population parameters and the corresponding sample statistic due to mistakes that occur when collecting, recording and tabulating the data. Sums of Random Variables Ex: Suppose you were supposed to read X pages for one class and Y pages for another class. X and Y are random variables . X + Y is also a random variable. The Expected Value of the sum of the two random variables is: E[X + Y] = E[X] + E[Y]. If X and Y are independent then the variance of the sum of the two random variables is: Var[X + Y ]= Var[X] + Var[Y]. If X and Y are independent random variables and they follow normal distributions with parameters (ux, ox^2) and (uy, oy^2) then X + Y follows a normal distribution with parameters (ux + uy, ox^2 + oy^2)....
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