## A simulation study: the statistical power of normality tests

We will conduct a simulation study to investigate the power of the goodness-of-fit tests:

-   Kolmogorov-Smirnov
-   Chi-squared
-   Lilliesfors
-   Shapiro-Wilk

1.  Generate samples of size $n = {5,10,20,40,80,160,320,500,1000}$ from:

-   Chi-squared distribution with df=3
-   Student's t-Distribution df=4
-   Exponential distribution with scale parameter of 1
-   Uniform distribution in (0,1)

2.  Apply the goodness-of-fit tests above to test `normality` and find the power (probability of rejecting the null hypothesis) for each of the tests.

3.  Plot the results. The sample size (x-axis) vs the power (y-axis) for each test.

```{r}

```
4. Comments on the results and provide recommendations for each case.