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. the sample is less than 5% of the population
  3. lb is .14 and ub is .16
  4. the chance that the porportion of american adults 18 yrs and older who have used their smart phones to purchase soemthing between .14 and .16 is 90%.

26.

  1. 0.43
  2. yes n is less than 5% 282.6 >10
  3. lb is .401 and ub is .459
  4. they are 95% confident that the population porportion of workers and retires in the u.s 25 years of age and older who have less than $10,000 in savings is between .402 and .459

27.

  1. .519
  2. yes sample is less than 5% and 250.39 is >10
  3. lb: .45 , ub : 550
  4. Type answeryes it is possible because itc could be outside of the confidence interval, it is not likely
  5. lb : .450 ub: .512

28.

  1. .75
  2. yes the requirements are satisfied 192 > 10 and sample is less than 5%
  3. LB : .715 and UB: .785
  4. it is possible but unlikely because the lower bound is not less than .7 or 70%

  5. lb is .236 and ub is .264 29.

  6. .540
  7. yes the sample is less than 5% of the population
  8. lb: .520 ub:.571
  9. lb : .509 and ub : .571

  10. as the area of confidence increases the interval widens