Use R to generate n 5 observations from the Normal distribu

Use R to generate n = 5 observations from the Normal distribution N(20,5). Test H_0 : mu = 20 versus H_a : 20 at the alpha = 0.05 significance level. Repeat this process 100 times and then count the number of times that you reject H_0. Explain your results.

Solution

Use the following code -

So, we see that the null hypothesis is rejected all the 100 times.

This is because the sample size is very small. And the variance is a bit high.