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Q1.Central limit theorem allows us to use a sample from a population to draw certain statistical conclusions about the entire population since in most cases it is not very practical to sample the entire population (Wonnacott and Ronald 120). Using the applet simulator I created…
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Download file to see previous pages When the sample size (N) is small it takes a larger number of sample (Reps > 1000) to see that the distribution is normal while when N is relatively larger it takes relatively smaller number of sample (reps< 1000) to realize a normal distribution. When a population of a uniform shape is used a normal curve of sample mean is still realized. With a skew population shape, the sample mean is skewed but tending towards normal distribution with a reduced skew as opposed to the skew of the population and does not have any outlier even when entire population have outliers.
In conclusion, if the parent population is normal, the sampling distribution will always be normally distributed. If the population is not normal, the distribution of the sample mean will be approximately normally distributed if the sample size is large enough. From this we learn that this statistical technique assumes normality even when we are sampling populations that are not normal distributions. Hence we can say that central limit theorem is a statistical technique that assumes normality in both normal and normal statistical distribution shapes. When the sample size is large enough, the sampling distribution of the sample mean will always tend to normal distribution.
In the first sentence it will be better to say that the central limit theorem describes the characteristics of the sampling distribution of the mean of samples that are randomly sampled from a population. Instead of saying “the means sample means is approximately normal” we rather say that the distribution of the mean of the sample is normal. And lastly there is a spelling mistake in the first paragraph last sentence. Instead of “…the sampling distribution if the mean approves a normal distribution…” it read “…the sampling distribution of the mean approves a normal distribution…”
Here, the classmate has done extremely well to point out that as the sample ...Download file to see next pagesRead More
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