document.write( "Question 1179168: A population consists of the five numbers 2, 3, 6, 8, 11. Consider all possible samples of size two which can be drawn with replacement from this population. Find (a) the mean of the population, (b) the standard deviation of the population, (c) the mean of the sampling distribution of means, (d) the standard deviation of the sampling distribution of means, i.e., the standard error of means. \n" ); document.write( "
Algebra.Com's Answer #808726 by Edwin McCravy(20056)\"\" \"About 
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document.write( "mean of population = \"%282%2B3%2B6%2B8%2B11%29%2F5=30%2F5=6\"\r\n" );
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document.write( "variance of population = [(2-6)²+(3-6)²+(6-6)²+(8-6)²+(11-6)²]/5 = 10.8\r\n" );
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document.write( "standard deviation of population = √(var) = √(10.8) = 3.286335345\r\n" );
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document.write( "  [2,2]  mean = 2    var =  0\r\n" );
document.write( "  [2,3]  mean = 2.5  var =  0.25\r\n" );
document.write( "  [2,6]  mean = 4    var =  4\r\n" );
document.write( "  [2,8]  mean = 5    var =  9\r\n" );
document.write( " [2,11]  mean = 6.5  var = 20.25\r\n" );
document.write( "  [3,3]  mean = 3    var =  0\r\n" );
document.write( "  [3,6]  mean = 4.5  var =  2.25\r\n" );
document.write( "  [3,8]  mean = 5.5  var =  6.25\r\n" );
document.write( " [3,11]  mean = 7    var = 16\r\n" );
document.write( "  [6,6]  mean = 6    var =  0\r\n" );
document.write( "  [6,8]  mean = 7    var =  1\r\n" );
document.write( " [6,11]  mean = 8.5  var =  6.25\r\n" );
document.write( "  [8,8]  mean = 8    var =  0\r\n" );
document.write( " [8,11]  mean = 9.5  var =  2.25\r\n" );
document.write( "[11,11]  mean = 11   var =  0\r\n" );
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document.write( " sums           90         67.5\r\n" );
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document.write( "mean of sample means = 90/15 = 6\r\n" );
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document.write( "variance of sample means = 67.5/5 = 13.5\r\n" );
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document.write( "standard deviation of sample means = √13.5 = 3.674234614\r\n" );
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document.write( "(a) the mean of the population, μ=6\r\n" );
document.write( "(b) the standard deviation of the population, σ=3.286335345\r\n" );
document.write( "(c) the mean of the sampling distribution of means, μx̄=6\r\n" );
document.write( "(d) the standard deviation of the sampling distribution of means, i.e., the\r\n" );
document.write( "standard error of means. σx̄=3.674234614\r\n" );
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document.write( "Edwin
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