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. .181.
  2. 341.84 > 10.
  3. Lower:.168, Upper:.194.
  4. 90% confident that the population of Americans 18 years or older have donated blood within the past 2 years is between .168 and .194.

26.

  1. .430.
  2. 282.60 >10.
  3. lower.401. upper .459
  4. we are 95% confident that workers and retirees in the US 25 or older who have 10,000 in savings is between .401 and .459.

27.

  1. .519.
  2. 250.39 >10.
  3. lower .488, upper .550.
  4. it is possible because there is a polsibility it was not captured, but it is not likeley becasue .6 is outside of the confidence interval.
  5. lower .450, upper .512.

28.

  1. .75.
  2. 192 > 10.
  3. lower .715, upper .785.
  4. yes it is possible, but it is unlikely because .7 is outside of the interval.
  5. lower.219, upper .288.

29.

  1. lower .071, upper .151.
  2. lower ..058, upper .164.
  3. as the confidences increases te margin or error increases.