Question 8.236

59. Hawaii Residents Thriving. The Gallup Organization collects data on the well-being of residents in the 50 states. In 2011, the highest proportion of residents that are reported to be “thriving” is in Hawaii, with 65.5% thriving. (Gallup categorizes respondents as thriving who report fewer health problems; fewer sick days; lower levels of stress, sadness, and anger; and higher levels of happiness and respect.) Suppose the poll is based on 1000 Hawaii residents.18

  1. Find the margin of error using a 99% confidence level. What does this number mean?
  2. Construct and interpret a 99% confidence interval for the population proportion of all Hawaiians who are thriving.

8.3.59

(a) 0.0387 (b) We can estimate the population proportion of Hawaii residents who are thriving to within 0.0387 with 99% confidence. (c) (0.6163, 0.6937) (d) We are 99% confident that , the population proportion of Hawaii residents who are thriving, lies between 0.6163 and 0.6937.