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. Random sample, n x p hat x (1 - p hat) = 341.8 > or equal to 10, and the sample is less than 5% of the population
  3. Lower bound: 0.168 Upper bound: 0.194
  4. 90% confident that the proportion of Americans aged 18 or older who have donated blood in past few years is between 0.168 and 0.194

26.

  1. 0.430
  2. Random sample, n x p hat x (1 - p hat) = 282.6 > or equal to 10, and the sample is less than 5% of the population
  3. Lower bound: 0.401 Upper bound: 0.459
  4. 95% confident that the proportion of working and retired Americans aged 25 or older who have less than 10000 dollars in savings is between 0.401 and 0.459

27.

  1. 0.519
  2. Random sample, n x p hat x (1 - p hat) = 250.39 > or equal to 10, and the sample is less than 5% of the population
  3. Lower bound: 0.488 Upper bound: 0.550
  4. Yes, it is possible that the population proportion exceeds 60% because it is possible that the true proportion isn’t captured in the confidence interval. This is however unlikely.
  5. Lower bound: 0.450 Upper bound: 0.512

28.

  1. 0.750
  2. Random sample, n x p hat x (1 - p hat) = 192 > or equal to 10, and the sample is less than 5% of the population
  3. Lower bound: 0.715 Upper bound: 0.785
  4. Yes, it is possible that the population proportion is below 70% because it is possible that the true proportion isn’t captured in the confidence interval. This is however unlikely.
  5. Lower bound: 0.215 Upper bound: 0.285

29.

  1. Lower bound: 0.071 Upper bound: 0.151
  2. Lower bound: 0.058 Upper bound: 0.164
  3. As the level of confidence increases, the lenght of interval increases.