Answer the free response question below

3. At a company picnic, many of the attendees became ill the next day. The manager suspects that the illness may be related to the potato salad. which was in the sun for a long period of time. The manager was able to contact [20 attendees and classied each person according to whether or not the person got sick and whether or not the person ate the potato salad. The table shows the results. Ate the potato salad? a) 2 points '3) 4 Points Got sick? c) 4 points (a) Calculate the difference in the proportion of attendees that got sick between the two groups (ate the potato salad - did not eat the potato salad). One hundred trials of a simulation were performed to see what differences in proportions would occur due to only chance variation, assuming that the potato salad is not related to getting sick. That is, the 43 attendees that got sick and the 77 attendees that did not get sick were randomly assigned to two groups of size 70 and 50. The results of the simulation are shown below. 0000000000000 0000000000000000 0000000000000 0000 000000 0000000000 0000000000 0000000000 00000 000000 00000 0.3 0.25 O.2 0.15 -0.l 0.05 0 0.05 0.1 0.15 02 Simulated dierelee in sample proportion of attendees that got siclt (b) There is one dot at 0.209. Explain what this dot means in this context. (0) Use the results of the simulation to determine if the difference in proportions from part (a) is statistically signicant. Explain your reasoning