1. A 2. The 72% because of selection bias (explain what selection bias is for full credit) While the newspaper sample is considerably smaller in size, it is arguably more scientific because respondents were selected using a random probability method. 3. The standard error is root(361) * root(.75 * .25) --------------------------- 361 multiplied by 100 you should get 2.279% 4. It is possible and it should be 75% +/- the standard error calculated in #3. (4.558) 5. This is a SE of a sum. The box average is (+9 * .1) + (-5 * .3) +( 0 * .6) = -.60 so the expected value is -.60 * 100 = -60 dollars the standard deviation is the square root of: (9 - (-.60))^2 + 3*(-5 - (-.60))^2 + 6*(0 - (-.60))^2 ------------------------------------------------------ 10 or $3.9038 so the standard error is 10*3.9038 or $39.038 6. You lost $158, this is -158 and you were only expecting to lose $60 (-60). Need to calculate Z to find the chance of seeing this kind of outcome: Z = -158 - (-60) ------------ 39.038 = -2.51, round down to -2.5, the area to left of -2.5 is .62%. So there was about a .6% or 6 in 1000 chance of losing $158 or more 7. Here, the population is known and you're being asked about the chance of seeing a particular sample outcome -- specifically between 5% and 9%. Need a Z score Z = 9% - 10% ------------------------------------- = -.366 or about -.35 (root 121) * (root .10 * .90) ------------------------ * 100 121 Z = 5% - 10% ------------------------------------- = -1.83 or about -1.80 (root 121) * (root .10 * .90) ------------------------ * 100 121 The area associated with a Z = -1.80 is 92.81% The area associated with a Z = -.35 is 27.37% Take the difference in this case and divide by 2 to give 32.72%