Paragraph Styles A recent Gallup Poll asked a simple random sample of 1600 American adults, "Have you, yourself smoked any cigarettes in the past week?" Suppose that in fact 20% of all American adults would answer "yes" if asked this question. The proportion p of the sample who answers "yes" will vary in repeated sampling. To investigate this, we simulated 1000 samples of size > = 1600 from a population in which 20% would answer "yes" they smoked cigarettes in the past week. The results of this simulation are provided in the table below. Please fill in the percentage column and write your answers as decimals rounded to three places. (The first two have been done for you as an example.) Class for p Frequency (of the 1000 samples) Percentage 0.165 to 0.170 1 0.001 0.170 to 0.175 6 0.006 0.175 to 0.180 22 0.180 to 0.185 58 0.185 to 0.190 89 0.190 to 0.195 146 0.195 to 0.200 178 0.200 to 0.205 182 0.205 to 0.210 160 0.210 to 0.215 81 0.215 to 0.220 49 0.220 to 0.225 17 0.225 to 0.230 7 0.230 to 0.235 43. Find probability that between 0.18 and 0.22 of the sample smokes: a) Using the 68-95-99.7 Rule. Make sure to sketch the density curve and shade the area of interest. b) Using the results of the simulation. (HINT: Use the table you completed on page one!) 4. Are the results for parts a) and b) EXACTLY the same for questions #1, #2, #3 above? 5. Why is there a difference between the results for parts a) and b) for each question above? 6. What would happen to the results for parts a) and b) if we simulated 50000 samples of size n = 1600 from a population in which 20% would answer "yes" they smoked cigarettes in the past week. 7. What statistical principle explains the answers to questions #5 and #6? (Circle your answer) 68-95-99.7 Rule The Law of Large Numbers The Law of Lucky Results