9.1

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. .15
  2. proportion (542/3611) and sample size are given
  3. .14~.16
  4. 90% confidence that the number of americans who used a smartphone to make a purchase is between .14 and .16

26.

  1. .43
  2. proportion, sample size
  3. .40~.46
  4. 95% confident that .4 to .46 americans have less than 10,000 in savings.

27.

  1. .52
  2. proportion and sample size
  3. .49~.52
  4. no
  5. .45~.51

28.

  1. .75 (b)proportion and sample size
  2. .7054~.7946
  3. yes, no
  4. .2054~.2946

29.

  1. .54
  2. proportion and sample size
  3. .52~.56
  4. .5~.58
  5. there are more possibilities.

9.2

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 \(\bar{x} = 18.4\), sample standard deviation is 4.5, sample size = 35, and your confidence level is 95% this is how you can have R calculate a Confidence Interval for you.

conf_int(xbar = 18.4, size = 35, conf = .95, s = 4.5)
## [1] 16.8542 19.9458

21.

  1. 1.85~19.94
  2. 17.12~19.68
  3. 16.32~20.47

23.

(a)32.78~37.42 (b) 33.66~36.54 (c) 31.76~38.44 (d)

25. 90% confidence that the customers take between 161 and 164 seconds to serve at a drive through.

27. 1. more subjects, 2. higher confidence interval.

29.

  1. the histogram is right skewed because people who had more to drink are also more liekly to crash while driving.
  2. proportion and sample size
  3. .164~.169
  4. It is not possible.

31. 12.05~14.75

33. 1.084~8.11

9.3

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 you sample standard deviation s = 2, the sample size = 35, and your confidence level is 95% this is how you can have R calculate a Confidence Interval for \(\sigma\).

conf_sig(s = 2, size = 35, conf = .95)
## [1] 1.617744 2.620404

5

10.117, 30. 144

7 9.542, 40.289

9

  1. 7.94, 23.66
  2. 8.59, 20.63 width decreases
  3. 6.61, 31.36, width increases

11

1.612, 4.278. 95% CONFIDENT THAT SD IS BETWEEN 1.612 AND 4.278

13

849.7, 1655.3, 90% confident that sd is between 849.7, and 1655.3,