## find the probability that our hypothesis is true.

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.

### Determine the outlet concentration x1 in the water solution and in the trichloroethane solution using an analytical equation.

Predicting Extraction for an Existing Tower with a Given Number of Steps. An existing tower contains 5.0 theoretical steps. It is desired to predict its performance under the following conditions….

### Calculate the minimum solvent that can be used. [Hint: In this case, the tie line through the feed L0 represents the condition for minimum solvent flow rate.

Minimum Solvent and Countercurrent Extraction of Acetone. An aqueous feed solution of 1000 kg/h containing 23.5 wt % acetone and 76.5 wt % water is being extracted in a countercurrent….

### Determine the break-point time, the fraction of total capacity used up to the break point, the length of the unused bed, and the saturation loading capacity of the solid.

Drying of Nitrogen and Scale-Up of a Column. Using molecular sieves, water vapor was removed from nitrogen gas in a packed bed (C1) at 28.3°C. The column height was 0.268….