1. Generate 1000 random samples of size 40 from the normal distribution with mean µ = 3 and
standard deviation σ = 2. Compute 95% the confidence interval of 1000 samples and find the rate
of confidence interval contains the true mean. What did you learn from this simulation study?
2. For each of the distributions below, generate a random sample of size 100 and then plot the normal
probability plot (based on manual algorithm instead of built in function) of each data and discuss.
* (a) t-distribution (df=1)
* (b) t-distribution (df=10)
* (c) t-distribution (df=100)
* (d) standard normal distribution
3. Conduct the exercise 7.33 by R. Also, when you verify the normality assumption in part (b) of 7.33,
use both box-plot and normal probability plot.