Question 7.100

70. A random sample of 2454 twelfth-grade American students responded to the following question: “Taking all things together, how would you say things are these days—would you say you’re happy or not too happy?” Of the responses, 2098 students selected “happy.”

  1. Calculate a 95% confidence interval for the population proportion of twelfth-grade American students who are happy.
  2. Would a 97% confidence interval for the proportion of happy students be wider or narrower than the one you calculated for part (a)? Justify your answer.