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Q. Suppose a study is being done and the population is the American public. How would you go about choosing a random sample population to phone for a survey?
Solution: One way to choose a random sample population is by using a random number generator. First, list all telephone exchanges in America. Then use the random number generator to randomly dial a 7-digit number within these exchanges. What this method does essentially is create a list of all possible household phone numbers in America and then select a subset of numbers from that list for the sample population. (This is the method used for Gallup polls).
Notice that there are the limitations of this method. There are Americans who are not living in households with phone numbers (homeless or without phone). There are Americans who are not living in America or who might be traveling during the time of the sampling.
Consider a multiple regression model Y=ß0+ß1X1+ß2X2+µ The sample data yields the following matrices: X’X= { ¦(33&0&0@0&40&0@0&20&60) } Y’X=¦((132&24&92)) ?(y-Y)2 =150 a. what
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List all possible simple random samples of size n = 2 that can be selected from the population {0, 1, 2, 3, 4}. Calculate 2 s for the population and Var y( ) for the sample.
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