2. Hypothesis in using the descriptive statistics (9 points) Let's think about the house price. According to the Case-Shiller Home Price Indices in 2020, Chicago and San Francisco have following sample mean and population standard deviations (the sample mean was calculated by daily base, so the sample size (n) was 30): CHICAGO San Francisco Sample Mean 170.55 182.47 Population Standard Deviation 10 15 1) Using hypothesis test, prove if these house price indices between Chicago and San Francisco are same. (Setup a hypothesis, show your works to perform the test, and state your verdict) 2) Some people argue that San Francisco has higher house price than that of Chicago based on the index. Prove/disprove the argument using a hypothesis test. 3) Let's assume the population standard deviations are unknown, and the sample standard deviation of for Chicago is 11.5 and that of San Francisco is 13.3. Some people argue that San Francisco has higher variability (higher variance) in house prices than that of Chicago. Setup a hypothesis, perform the test and prove/disprove the argument