Lab 6: Sampling distributions and the Central Limit Theorem 1. The distribution of the sample mean is not approximately normal. There is curvature to the normal probability plot. The superimposed bell curve does not match with the histogram and there is more of a bell shape in the probability plot than the histogram.
2. The shape of the distribution with sample size 100 is very similar to the bell curve. Its normal probability plot supports this by being linear and showing it fits the normal distribution curve. This supports the Central Limit Theorem as the theorem states that as the sample size increases, the sample means distributions will be similar to that of a normal distribution. Even with the sample size of 5, its normal probability plot shows a bit more linearity than the plot with a sample size of 2. 3. The maximum value of web pages visited is 74. The mean is 4.667 and the standard deviation is 6.313. The distribution is definitely not normal. There is no linearity to the normal distribution plot and the bell curve does not match with the histogram whatsoever. 4. The three sample means are 2.4, 4.5, and 3.1. Compared to the population mean, the second mean is relatively close, but the first and third value are much smaller than the mean. 5. With the 100 sample means, the mean is 4.726 and the standard deviation is 1.903. 6. The expected mean is 4.726 and the expected standard deviation is .602. While the mean stays the same, the standard deviation in a sample size of 10 is smaller than the standard
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