#4) Go to the following website: http://wwwJtcconline.net/greenliava/Statistics
ID: 3051421 • Letter: #
Question
#4) Go to the following website: http://wwwJtcconline.net/greenliava/Statistics clt/cltsimulation.html Run simulations by first clicking on a population distribution (Uniform, Left-Skewed, Right-skewed, or Normal), then click on each sample size (n-2, n-9, n 25, n 36, and n 100). Click "New Dist" to switch to a different distribution. a) For each population distribution, how large of sample is needed to obtain an approximate normal sampling distribution of Compare the population mean and standard deviation (on the top graph) to the mean and standard deviation of the simulated distribution (on the bottom graph). How do the means compare? How do the standard deviations comparei? b) OVER>
Explanation / Answer
a. A normal distribution is one where the distribution is symmetric about the mean and 95% of all the values fall within 1.96 std deviatons from the mean with an approximately smooth curve
For each population distribution (Uniform, Right skewed, left Skewed and Normal) the distribution starts tending towards a normal distribution with increasing sample size. The sample size at which the above definition of a normal distribution started to become true was approximately at n=30. Hence a sample size of at least 30 is needed to obtain a normal sampling distribution
b. The mean and std. deviation of the bottom graph as compared to the top graph exhibited these changes as follows
The mean was initially higher or lower than the mean given in the top grpah, but as the sample size increased, the mean of the lower graph tended towards the mean shown in the top graph and finally became equal to it at large sample sizes. The std. Deviation on the other hand, in the lower graph started to decrease with increase in sample size
This proves that sampling distributions with a larger sample size are are more representative of the population mean and std. deviations.
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