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If you randomly divide a group of 300 flu patients into two groups, where one group gets a placebo and the other gets a new medicine, you are conducting an observational study.

A certain stock lost 70% of its value yesterday, but it jumped up 90% today. Calculate how much (what %) the stock went up or down in value during the two-day period.  Write ONLY your answer(s) in the box below. On your own paper, show all your work and justify your answer(s). You will be submitting the paper at the end of this test. 

What is log (10,000)?

A box office was having a sale, and a great seat was available for $180, which was 40% off the regular ticket price. How much was the regular price?  Write ONLY your answer(s) in the box below. On your own paper, show all your work and justify your answer(s). You will be submitting the paper at the end of this test. 

In an election with 5 candidates, it is possible that there is no Condorcet winner.

In a sociology study, researchers have discovered that children who play the violin while in middle school end up earning more money as adults. Therefore, it is valid to conclude that playing the violin leads to higher income. 

A city has three libraries and 15 librarians. Use Hamilton’s Method to determine how many librarians each library should get. (Hint: first, find the standard divisor.) Library Residents Quota Min. Q. Remainder Librarians East 3200 South 4500 North 7300 15,000 Write ONLY your answers (the right column) in the box below. On your own paper, show all your work and justify your answers. You will be submitting the paper at the end of this test. You should copy the entire table.    

The following options are available for a mortgage:  [Option 1] 30-year mortgage with monthly payments of $1818.60. [Option 2] 15-year mortgage with monthly payments of $2879.21.  How much will you save overall (for the term of the mortgage) by choosing Option 2 (the shorter loan) compared to Option 1? Write ONLY your answer(s) in the box below. On your own paper, show all your work and justify your answer(s). You will be submitting the paper at the end of this test. 

Hamilton’s Method of apportionment is the fairest of all because it favors more popular states.

A market researcher is surveying 50 people he met in a shopping mall when he went there last Thursday afternoon. Which sampling method is used here?