If your \(x = 542\) (ie the number of “successes” and your \(n = 3611\), this is how you can have R calculate a 90% Confidence Interval for you.

binom.test(x = 542, n = 3611,  conf.level = .90)[["conf.int"]]
## [1] 0.1403939 0.1602214
## attr(,"conf.level")
## [1] 0.9

25.

  1. 0.181
  2. 241.84 is greater than 10 and the sample is less than 5% of the population.
  3. lower bound=0.168, upper bound=0.194
  4. We are 90% confident that the population proportion of adult Americans who have donated blood in the past two years is between 0.168 and 0.194.

26.

  1. 0.43
  2. 286.6 is greater than 10 and the sample is less than 5% of the population.
  3. lower bound=0.401, upper bound=0.459
  4. We are 95% confident that the population proportion of workers and retirees in the US 23 years of age and older who have less than $10,000 in savings is between 0.401 and 0.459.

27.

  1. 0.519
  2. 250.39 is greater than 10 and the sample is less than 5% of the population.
  3. lower bound=0.488, upper bound=0.550
  4. It is possible but not likely because it is outside the confidence interval.
  5. lower bound=0.450, upper bound=0.512

28.

  1. .75
  2. 192 is greater than 10 and the sample is less than 5% of the population.
  3. lower bound=0.715, upper bound=0.785
  4. It is possible, but unlikely because its outside the confidence interval.
  5. lower bound=0.215, upper bound=.285

29.

  1. lower bound=0.071, upper bound=0.151
  2. lower bound=0.058, upper bound=0.164
  3. Increasing confidence level causes the margin of error to increase as well.