1 - Statistics 144 Sample Midterm Solutions Fall Quarter...

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Unformatted text preview: Statistics 144 Sample Midterm Solutions Fall Quarter 2009 PROBLEM 1 Suppose a population of N = 6 units has the following values y 1 = 10, y 2 = 6, y 3 = 9, y 4 = 11, y 5 = 17 and y 6 = 14. Suppose, we take a sample of size n = 3 (a) Give the sampling distribution of the sample total. There are ( 6 3 ) = 20 different samples. t S 25 26 27 29 30 31 32 33 y 8.33 8.67 9 9.67 10 10.33 10.67 11 f ( S ) 0.05 0.05 0.05 0.05 0.10 0.05 0.05 0.10 t S 34 35 36 37 38 40 41 42 y 11.33 11.67 12 12.33 12.67 13.33 13.67 14 f ( S ) 0.10 0.05 0.05 0.10 0.05 0.05 0.05 0.05 Total: t y = 67 Mean: y U = 11 . 17 Variance: S 2 = 14 . 97 (b) Give an estimate for the population total and show that it is unbiased. Total: t y = 67 estimated by t y = 6 y = 6 3 t S E ( t y ) = 6 3 E ( y ) = 6 3 ( 25 . 05 + 26 . 05 + ... + 41 . 05 + 42 . 05 ) = 67 (c) Calculate its standard error using the sampling distribution and compare it to the formula given in class. SE ( t y ) = 36 9 ( 25 2 . 05 + 26 2 . 05 + ... + 41 2 . 05 + 42 2 . 05 )- 67 2 = 9 . 476 Formula in class SE ( t y ) = N ( 1- n N ) S n = 9 . 476 PROBLEM 2 The table below gives the number of refereed publications of a sample of 50 faculty (N=807) at a university. Assume a SRS was taken.(N=807) at a university....
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1 - Statistics 144 Sample Midterm Solutions Fall Quarter...

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