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. 0.150
  2. 460.40 is greater than or equal to 10, so the sample size is less than 5% of the population.
  3. Lower bound = 0.140; Upper bound = 0.160
  4. We are 90% confident that the proportion of Americans 18 years or older who use their smartphones to make purchases is between 0.140 and 0.160.

26.

  1. 0.430
  2. 282.60 is greater than or equal to 10, so the sample size 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 United States 25 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 or equal to 10, so the sample size is less than 5% of the population.
  3. Lower bound = 0.488; Upper bound = 0.550
  4. It is possible that a supermajority of more than 60% of adult Americans believe that television is a luxury they could do without, since it is possible that the true proportion is not captured in the confidence interval. However, it is not likely.
  5. Lower bound = 0.450; Upper bound = 0.512

28.

  1. 0.75
  2. 192 is greater than or equal to 10, so the sample size is less than 5% of the population.
  3. Lower bound = 0.717; Upper bound = 0.783
  4. It is possible that the proportion of adult Americans aged 18 or older in which the issue of family values is very important in determining their vote for president is below 70%. It is likely.
  5. Lower bound = 0.217; Upper bound = 0.283

29.

  1. 0.540
  2. 434.20 is greater than or equal to 10, so that sample size is less than 5% of the population.
  3. Lower bound = 0.52; Upper bound = 0.56
  4. Lower bound = 0.509; Upper bound = 0.571
  5. Increasing the level of confidence will widen the interval.