Problem 1. 

Consider the two data sets q1.txt and q2.txt. . For each data set, do the following exercises:

1. Find the mean and variance of the sample data
2. Find the median, first, second, and third quartile of the sample data
3. Plot the sample data using a histogram
4. Draw the quantile plot for the sample data
5. Compare the distribution of the sample data against the theoretical normal distribution using a Q-Q plot

Problem 2. 

Consider the population data in the file normal.txt. This data is normally distributed.

1. Find the population mean and variance
2. Generate a random sample of size 50. (i.e. randomly select 50 numbers from the population). Find a 90% and 95% confidence interval for the mean. Is the population mean within the intervals?
3. Generate a random sample of size 10. (i.e. randomly select 10 numbers from the population). Find a 90% and 95% confidence interval for the mean. Is the population mean within the intervals?
4. Repeat the exercise above for the population data in the file not-normal.txt. This data is not normally distributed. For the smaller sample (size 10), compute the confidence intervals with and without normalization.