## Monday, August 12, 2019

### Discussion Questions Week 4 Essay Example | Topics and Well Written Essays - 500 words

Discussion Questions Week 4 - Essay Example By the central limit theorem, by performing the experiment many times, I would end up with a normal distribution, and at very high numbers of experiments, the mean, the mode and the median scores would all tend to be 50 Ã¢â‚¬â€œ or a perfect Bells curve. The jaggedness and asymmetry of the curve would also disappear on numerous repetitions of the experiment. 2. Confidence intervals apply to samples ( in the above example, the 100 toss batches) drawn from a large population ( a very large number of batches thrown) . It means the range of scores ( say 45 Ã¢â‚¬â€œ 55 in the above example), when the population mean of 50 is likely to be present in a high proportion of cases. In normal statistical work an arbitrary figure, 95 % is taken as the proportion to define the confidence intervals, which is referred to as the confidence level. The most controllable method to increase the precision (narrowing) of the confidence interval is to increase the sample size. For instance, in the current example, if the coin is thrown a 1000 times every batch, the confidence intervals could be significantly narrowed (say, 48 Ã¢â‚¬â€œ 52). Even if we assume that the sample size of 1100 is normally distributed ( although in polls like this it is rarely so) and that the sample mean of 572 is a true estimation of a population which votes for the mayor by a majority, we can than then test the null hypothesis that this sample H1 is different from a larger population sample H0 where the mayor only has a 50 % chance of winning ( sample mean 550). Let us assume (1) that the standard deviation of the samples is 11, as then, the sample mean of H1 is just within 2 standard deviations away from the population mean of 550 ( i.e. 550 +