Repeat the above example, but this time use the hierarchical clustering approach with complete linkage as a measure of distance between clusters. Create three clusters (i.e., K=3) based on your hierarchical cluster analysis and add a new variable to the data-identifying cluster ids. Using a contingency table, explain how the three identified clusters are related to the three species of flowers.

1. Suppose that the smoking status, X, has Bernoulli(μ) distribution, where the prior distribution for μ is Beta(1,10). We have interviewed a random sample of 50 people and found that 8 of them smoke regularly. Find the posterior distribution of μ given the observed data. Plot the posterior distribution and find the 95% credible interval for μ. What is the point estimate for μ based on this distribution? Compare this point estimate to the sample proportion, which is also commonly used as a point estimate for the population proportion. Suppose that we hypothesize that less than 20% of the population smoke. Use the posterior probability distribution to find the probability that our hypothesis is true.