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Stat 215 Assignment 13

# Stat 215 Assignment 13 - Stat 215 Assignment 13 Module CLT...

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Stat 215 Assignment 13 Module: CLT , Exercise: SampDistrShape Objective : (not available) Problem Description : This exercise illustrates the effect of the sample size on the sampling distribution of the mean for parent distributions of various shapes. Display the CLT Java applet to answer the following quesitons: Question Generate a histogram of means based on 2000 samples of size n=3 from a normal distribution and compare the resulting histogram to the curve of a normal distribution. Does the histogram seem to follow a normal distribution? Explain. Answer Yes the histogram does seem to follow a normal distribution, although there seems to be more area in the tails and less area near the center of the distribution compared with the normal distribution. The CLT says that, since the parent distribution is normal, the distribution of the samples should also be normal. Your Answer Yes, the curve seems normal with a few outliers above and a few below the normal line. Grader Comments (none) Grade 1.0 (out of 1.0) Total 8.3 (out of 10.0) Question Generate a histogram of means based on 2000 samples of size n=3 from a uniform distribution and compare the resulting histogram to the curve of a normal distribution. Does the histogram seem to follow a normal distribution? Explain. Answer Yes the histogram does seem to approximate a normal distribution, although there seems to be more area in the tails and less area near the center of the distribution compared with the normal distribution. The "excess" area in the tails arises form samples in which (most of) the observed data values come from the high side (or low side) of the uniform distribution. We cannot use the CLT to describe the sampling distribution since n is less than 30. Your Answer No, the curve does not fit the normal line in the center of the graph. Grader Comments (none) Grade 0.2 (out of 1.0) Total 8.3 (out of 10.0) Question Generate a histogram of means based on 2000 samples of size n=30 from a uniform distribution and compare the resulting histogram to the curve of a normal distribution. Does the histogram better approximate a normal distribution than when n=3? Explain.

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Stat 215 Assignment 13 - Stat 215 Assignment 13 Module CLT...

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