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Statistics Projects - March 6 2008

Statistics Projects - March 6 2008 - Grace Chen March 5...

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Grace Chen March 5, 2008 Stats 13/2A SOCR Lab Experiments Central Limit Theorem : Exercise 1 a. X indicates the values of the variable. The distribution column next to it shows the density at its corresponding X value. Data is the value of the stimulation. X bar is the values of the sample mean. The distribution shows the height of X bar, and data is the value of the stimulation. b. X=3.16 (3.16-5)/2 = -.92 (about 1 standard deviation) P(3.16<X<5)=P(-.92 <X< 0) = .50 – .1788 = .3212 c. Xbar=3.14 (3.14-5)/(2/sqrt16)= -3.72 (about 3.72 standard deviations – very far away) P(3.14< Xbar< 5)=P(-3.72 <Xbar< 5) = .5 – 0.0000 = .5000 d. Xbar will have a smaller standard deviation because its standard deviation is 2/sqrt(n)=2/4=.5. The standard deviation of X is 2. Therefore, X will have a flatter curve, while Xbar will have a taller, skinnier curve, with more values concentrated around the mean. e. The graph of the sample means looks normal centering around 5. The mean of the samples is 4.969. The standard deviation is around 0.497.
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