The chi-square test for normality discussed in Section is far from perfect. If the sample is too small, the test tends to accept the null hypothesis of normality for any population distribution even remotely bell-shaped; that is, it is not powerful in detecting nonnormality. On the other hand, if the sample is very large, it will tend to reject the null hypothesis of normality for any data set.’ Check this by using simulation. Simulate data from a normal distribution to illustrate that if the sample size is sufficiently large, there is a good chance that the null hypothesis will (wrongly) be rejected. Then simulate data from a nonnormal distribution (uniform or triangular, say) to illustrate that if the sample size is fairly small, there is a good chance that the null hypothesis will (wrongly) not be rejected. Summarize your findings in a short report.