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ENME 392 - Homework 7 - Sp12_Solutions

# ENME 392 - Homework 7 - Sp12_Solutions - ENME392 Spring...

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ENME392 Spring 2012 Homework 7 Solutions Total number of points: 100 The questions are a follow-up to last-week’s assignment: (80 pts) a) Group your number-of-heads data into 25 groups of 4 points by taking the results of the first 4 tosses, then the next 4, and so on. Calculate the average and the variance of the number of heads in these groups. Show the results of your calculations in a table. b) Make a histogram showing the frequency distribution of the average number of heads. Show your binned data. c) On the same plot, show the expected sampling frequency distribution. Show the results of your calculations in a table. d) On the same plot, show the binomial frequency distribution calculated in part (b) of last week’s homework assignment. The experimental data are expected to follow the sampling distribution X Z / n μ σ - = . The values to use here are m = 20, p = q = 0.5, μ = mp = 10, σ = sqrt(mpq) = 2.236, n = 4. The calculation in the z column was (L55 - \$O\$49)/(\$O\$50/SQRT(\$O\$53)) where L55 contained the value in the X column, \$O\$49 the mean, \$O\$50 the standard deviation, and \$O\$53 the value for n. The sampling probability was found using NORMDIST(M55,0,1,FALSE) where M55 contained the Z values. The sampling frequency was found by multiplying by 25.

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Experimental Sampling Dist. of Mean Bin Frequency X Z Sampling Probability Expected Sampling Frequency 5.5 0 0 -8.944 0.000 0.00 11.00 6.5 1 1 -8.050 0.000 0.00 11.50 7.5 0 2 -7.155 0.000 0.00 9.75 8.5 1 3 -6.261 0.000 0.00 9.25 9.5 8 4 -5.367 0.000 0.00 11.00 10.5 7 5 -4.472 0.000 0.00 9.75 11.5 7 6 -3.578 0.001 0.02 10.50 12.5 1 7 -2.683 0.011 0.27 9.50 More 0 8 -1.789 0.081 2.01 9.25 9 -0.894 0.267 6.69 9.25 25 10 0.000 0.399 9.97 8.25 11 0.894 0.267 6.69 10.00 12 1.789
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ENME 392 - Homework 7 - Sp12_Solutions - ENME392 Spring...

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