Age Group 2011 2012 2013 2014 Here is the same table, expressed as intersection probabilities: 2011 2013 2014 2011 Age Group 2012 Age Group 2012 2013 2014 20 - 24 20 - 24 0.027 0.02 0.025 0.031 3840 2830 3450 4380 25 - 34 25 - 34 0.057 0.051 0.058 0.051 8040 7160 8180 7180 35 - 44 0.057 0.055 0.058 0.055 35 - 44 8020 7670 8150 7680 45 - 54 0.064 45 - 54 0.068 0.06 0.057 9040 9490 8400 7970 55 - 64 55 - 64 0.042 0.045 0.04 0.048 5920 6320 5680 6670 65 and over 1210 65 and over 0.009 0.007 0.008 0.007 990 1120 970 Chart Title 9000 8000 -7000 6000 5000 4000 3000 2000 1000 I 85-54 35-44 25-34 55-64 20-24 65 and older 5. If year and age group were independent, what would be the probability of a 20 to 24 year old filing a claim in 2014? Does that number agree with the observed intersection? What does that tell you? 6. Suppose you randomly sample 30 claims in 2014. You want to know the probability that 15 of them are aged 45 to 54. What probability distribution would you use? What is the probability that any one claimant is in that age group? 7. Now that you know what probability distribution to use, how many of the 30 claimants from 2014 do you expect to be 45 to 54? 8. What is the standard deviation for that probability distribution? 9. What is our commonly accepted convention for a probability to be considered statistically unusual (also called "statistically significant")? 10. How many of the 30 claimants would have to be in that age group, before you reach statistical significance? If you saw that many, what would it tell you