A progressive college experiments with matching roommates at random, regardless of gender or how cool that person is (or you are). Suppose the joint distribution of gender and coolness is:   +----------------------------+   |           Cool       Lame  |   |----------------------------|   |  Boy   .0652174   .4728261 |   | Girl   .0108696    .451087 |   +----------------------------+ You hear that your roommate 'Ali' is a girl. Knowing this, what is the probability that 'Ali' is Cool? (Enter your answer to three decimal places: ex: 0.123)

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The map below shows the percentage change in housing prices from June 2014 to June 2015 in each of nine regions (U.S. Census divisions).+ Pacific 7.68 Mountain 7.17 West North Central 3.91 West South Central 6.92 East North Central 4.51 East South Central 4.88 Middle Atlantic 1.72 South Atlantic 6.12 New England 3.18 by You are choosing a region of the country to move to. Let E be the event that the region you choose saw a increase in housing prices of 4% or more, and let F be the event that the region you choose is on the east coast. Describe the event of EU F in words. You choose a region that saw an increase in housing prices of 4% or more or is on the east coast. You choose a region that saw a increase in housing prices of 4% or more and is on the east coast. List the outcomes of E UF. OEUF = {Pacific, Mountain, South Atlantic} EUF = {East North Central, South Atlantic, West North Central, Mountain, Pacific} EUF = {New England, Middle Atlantic, East North Central} EUF = {East North…

We are interested in looking at the effect of a baseball player’s free agent status on their salary. We look at 337 baseball players and categorize them as either having a high salary (above 2 million) or not, and as either being free agents or not. ------------------------------------- You also wonder if having a high batting average affects the salary of baseball players. You classify all 370 baseball players as having a high batting average if it is over .300. 1. What are the variables you are looking at? What are the possible categories within each variable? Which is the explanatory, and which is the response? 2. If we want to perform a χ2 test to see if there is a relationship between the two variables, what is our null and alternative hypothesis?