PS_3_and_Solutions

The first figure shows the results when we have 10000

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Unformatted text preview: is consistent with the normal probability curve with the same parameters, we overplot the corresponding normal curve on the histogram. The first figure shows the results when we have 10000 different samples of size 10. The 10000 sample means are depicted with a histogram. The normal curve has the parameters 5,3; 0,81 /10. We can see that the values in 4 16 March 2011 the x‐axis takes values approximately in the range of (4,0; 6,5). The second figure is obtained under the parameters 10000 and 50. We see the range in the x‐axis becomes approximately (4,8; 5,8) which is narrower than the previous figure. This means the variation in the sample decreases. Moreover, the theory indicates that the normal curve now has the following parameters: 5,3; 0,81 /50, which also says the variation in the sampling distribution should be smaller. 10000 The last figure uses the parameters and 200. We see the range of the x‐axis gets even tighter and the shape of the histogram and the normal curve are quite supporting each other. Hence we can say that as gets larger, the sampling distribution of the mean tends to the normal distribution and the variance of the distribution gets smaller. Therefore, when we have a sample from the population of with large sample size , the calculated sample mean estimate the population mean with very small deviation from the true value. END OF PS # 3 5...
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