You can use the following syntax to check your answers. Note the answers you get in R will not be EXACTLY the same you get by hand but they should be pretty close.

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. 0.15
  2. 460.6>10
  3. (0.14,0.16)
  4. It’s 90% confident to say that the proportion of adult Americans age 18 years and older who have used their smartphones to make a purchase is between 0.140 and 0.160.

26.

  1. 0.43
  2. 282.6>10
  3. (0.402,0.459)
  4. It’s 95% confident to say that the proportion of workers and retirees in the United States who have less than $10,000 in savings is between 0.402 and 0.459.

27.

  1. 0.519
  2. 250.4>10
  3. (0.489,0.550)
  4. Yes, because it is possible that the true proportion is not captured in the confidence interval. However, it is not likely that the true proportion is greater than 60%.
  5. (0.450, 0.511)

28.

  1. 0.75
  2. 192>10
  3. (0.715,0.785)
  4. Yes, because it is possible that the true proportion is not in the confidence interval. it’s 99% confident to say that the true proportion is (0.715, 0.785), but it is not likely that the proportion of adult Americans aged 18 or older for which the issue of family values is extremely or very important is below 70%.
  5. (0.215, 0.285)

29.

  1. 0.540
  2. 434.2>10
  3. (0.52,0.56)
  4. (0.509,0.571)
  5. Increasing the level of confidence makes the confidence interval wider.