TECHNOLOGY MOST ADMIRED POLLS Since 1946, the Gallup Organization has conducted a "most admired" poll. In 2012, 1038 randomly selected U.S. adults responded to the question below. The results are shown at the right. THE GALLUP ORGANIZATION Survey Question What man* that you have heard or read about, living today in any part of the world, do you admire most? And who is your second choice? Reprinted with permission from GALLUP. *Survey respondents are asked an identical question about most admired woman. ACTIVITIES 1. Use technology to find a 95% confidence interval for the population proportion that would have chosen each person as their most admired man. a. Barack Obama b. Nelson Mandela c. Mitt Romney 2. Use technology to find a 95% confidence interval for the population proportion that would have chose each person as their most admired women. a. Hillary Clinton b. Michelle Obama c. Oprah Winfrey 3. Find the minimum sample size needed to estimate with 95% confidence, the population proportion that would have chosen Barack Obama as their most admired man. Your estimate must be accurate within 2% of the population proportion. FORMATIVE: TECHNOLOGY ACTIVITY WWW.GALLUP.COM 2012 Survey Results Top Three Most Admired Men Name 1. Barack Obama 2. Nelson Mandela 3. Mitt Romney Percent Mentioning 30 3 2 Top Three Most Admired Women Name 1. Hillary Clinton 2. Michelle Obama 3. Oprah Winfrey Percent Mentioning 21 5 4 4. Use technology to simulate a most admired poll. Assume that the actual population proportion who most admire Hillary Clinton is 24%. Run the simulation several times using n = 1038. a. What is the least value you obtained for p? b. What was the greatest value you obtained for p? To do one simulation, press MATH, highlight PRB, select 7:randBin(and type in 1038, .24). The output is the number of successes in a survey of n = 1038 people. In this case, a "success" is choosing Hillary Clinton as your most admired female. (Note: it takes approximately one minute for the TI-84+ to do the calculation) To run the simulation 10 times, use 7:randBin(1038, .24, 10). (These simulations will take approximately 8 minutes.) The output is a list of the number of successes in each of the 10 simulations. Calculate p for each of the simulations. p is equal to: (number of successes)/1038. Use these 10 values of p to answer questions 4 and 5. 5. Is it probable that the population proportion who most admire Hillary Clinton is 24% or greater? Explain your reasoning.