A. We are interested in understanding the power of Kolmogorov-Smirnov (KS) and Shapiro-Wilk (SW) tests for testing the hypothesis that data is coming from normal distribution. To calculate the power of a test using simulation, we need to
assume a distribution under an alternative hypothesis,
assume the alternative is true
simulate a sample of size n from the alternative distribution
determine whether the test statistic based on this sample would reject the null hypothesis of normality
repeat the simulation many times (thousands) and see in what proportion of simulations we see the correct outcome – that, is rejection. That proportion is the estimate of probability of rejection given that the alternative is true; i.e. it is the estimate of the power.
Conduct this exercise for KS and SW tests, for sample sizes of n=30 and n=100 and for the following alternative distributions: Log-Normal(0,1), t-distribution with 3 degrees of freedom, t-distribution with 20 degrees of freedom. Comment on the results
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