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Sampling Error October 16, 2016 7.1 Sampling Error GOALS: 1. Consider mean and standard deviation of all the possible samples of a population. 2. Consider the distribution of all the sample means. 3. Understand that the sample mean is not expected to be exactly the same as the population mean. 4. Understand how the sample size relates to the sample standard deviation. 5. Understand how the sample size relates to the reliability of the sample mean as an approximation for the population mean. Study Ch. 7.1, # 17, ~11 Class Notes: Prof. G. Battaly, Westchester Community College, NY Class Notes Statistics Home Page 7.1 Sampling Error Homework Investigate how samples relate to populations. Use a contrived small population. Samples of 4 Print this page to use with the next several slides. x Samples of 2 Samples of 3 x x μ = ___ Class Notes: Prof. G. Battaly, Westchester Community College, NY Statistics Home Page © G. Battaly 2016 Class Notes Homework 1 Sampling Error October 16, 2016 7.1 Sampling Error NY Yankees, 2011 Stats Player C J R G S Robinson Cano Batting Average 302 Derek Jeter 297 Alex Rodriguez 276 Curtis Granderson 262 Nick Swisher 260 http://espn.go.com/mlb/team/stats/batting/_/name/nyy/newyorkyankees Consider this a population: Find μ and σ Class Notes: Prof. G. Battaly, Westchester Community College, NY Statistics Home Page 7.1 Sampling Error Class Notes Homework Samples of 2 x CJ CR Class Notes: Prof. G. Battaly, Westchester Community College, NY Statistics Home Page © G. Battaly 2016 Class Notes Homework 2 Sampling Error October 16, 2016 7.1 Sampling Error Samples of 3 Samples of 2 x μ = ___ CJ CR CG CS JR JG JS RG RS GS x 299.5 CJR CJG 289 282 281 286.5 279.5 278.5 269 268 261 279.4 10.65 Class Notes: Prof. G. Battaly, Westchester Community College, NY Class Notes Statistics Home Page 7.1 Sampling Error Samples of 2 Homework Samples of 3 x μ = ___ CJ CR CG CS JR JG JS RG RS GS 299.5 289 282 281 286.5 279.5 278.5 269 268 261 279.4 10.65 x CJR CJG CJS CRG CRS CGS JRG JRS JGS RGS 291.6 287 286.3 280 279.3 274.7 278.3 277.6 273 266 279.4 7.46 Class Notes: Prof. G. Battaly, Westchester Community College, NY Statistics Home Page © G. Battaly 2016 Class Notes Homework 3 Sampling Error October 16, 2016 7.1 Sampling Error Do a dot plot of the original data. (n=1) x x x x x μ = ___ n=1 260 280 270 290 300 Class Notes: Prof. G. Battaly, Westchester Community College, NY Class Notes Statistics Home Page Homework 7.1 Sampling Error Do a dot plot of the original data. (n=1) μ = ___ xx n=1 260 x x x 270 280 290 300 Class Notes: Prof. G. Battaly, Westchester Community College, NY Statistics Home Page © G. Battaly 2016 Class Notes Homework 4 Sampling Error October 16, 2016 7.1 Sampling Error Do a dot plot of the samples of size 2. (n=2) x x x x x x xx x x μ = ___ n=2 n=1 xx 260 x x x 270 280 290 300 Class Notes: Prof. G. Battaly, Westchester Community College, NY Class Notes Statistics Home Page 7.1 Sampling Error Homework Do a dot plot of the samples of size 2. (n=2) μ = ___ n=2 n=1 x xx xxxx xx xx x 260 270 280 290 x x x 300 Class Notes: Prof. G. Battaly, Westchester Community College, NY Statistics Home Page © G. Battaly 2016 Class Notes Homework 5 Sampling Error October 16, 2016 Do a dot plot of the x samples of size 3. (n=3) x x x x xx x xx 7.1 Sampling Error μ = ___ n=3 n=2 n=1 x xx xxxx xx xx x 260 270 280 290 x x x 300 Class Notes: Prof. G. Battaly, Westchester Community College, NY Class Notes Statistics Home Page Homework F: samples of size 4 7.1 Sampling Error JRGS CRGS μ = ___ n=3 n=2 n=1 x xx xxx xx x x xx xxxx xx x xx x x x 260 270 280 290 300 Class Notes: Prof. G. Battaly, Westchester Community College, NY Statistics Home Page © G. Battaly 2016 Class Notes Homework 6 Sampling Error October 16, 2016 Do a dot plot of the samples of size 4. (n=4) 7.1 Sampling Error JRGS 273.8 CRGS 275 CJGS 280.2 CJRS 283.7 CJRG 284.5 μ = ___ n=4 n=3 n=2 n=1 x x x x x xx xxx xx x x xx xxxx xx x xx x x x 260 270 280 290 300 279.4 7.46 x Class Notes: Prof. G. Battaly, Westchester Community College, NY Class Notes Statistics Home Page 7.1 Sampling Error Homework 279.4 10.65 Distributions using DOTPLOTS JRGS 273.8 CRGS 275 CJGS 280.2 CJRS 283.7 CJRG 284.5 μ = ___ n=4 n=3 n=2 n=1 279.4 4.91 xx xxx x xx xxx xx x x xx xxxx xx x xx x x x 260 270 280 290 300 Class Notes: Prof. G. Battaly, Westchester Community College, NY Statistics Home Page © G. Battaly 2016 Class Notes Homework 7 Sampling Error October 16, 2016 7.1 Sampling Error Distributions using BOXPLOTS from geogebra Class Notes: Prof. G. Battaly, Westchester Community College, NY Class Notes Statistics Home Page Homework 7.1 Sampling Error n=4 n=3 n=2 n=1 x x xx x x xx xxx xx x x xx xxxx xx x xx x x x 260 270 280 290 300 As n increases, the sample means cluster closer to true population mean When we find the mean of the sample means from all possible samples of a given size, n, the mean of the sample means = population mean. μ = μ x Class Notes: Prof. G. Battaly, Westchester Community College, NY Statistics Home Page © G. Battaly 2016 Class Notes Homework 8
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