9.2 21-33 odds

    1. (16.85, 19.95).
n = 35
xbar = 18.4
s = 4.5
t_critical = qt(.975, n - 1)
lower = xbar - t_critical*s/sqrt(n)
upper = xbar + t_critical*s/sqrt(n)
(answer = c(lower,upper))
## [1] 16.8542 19.9458
  1. (17.11, 19.69); as the sample size increases, the margin of error (E) decreases.
n = 50
xbar = 18.4
s = 4.5
t_critical = qt(.975, n - 1)
lower = xbar - t_critical*s/sqrt(n)
upper = xbar + t_critical*s/sqrt(n)

(answer = c(lower,upper))
## [1] 17.12111 19.67889
  1. (16.32, 20.48); as the level of confidence increases, the margin of error (E) increases.
n = 35
xbar = 18.4
s = 4.5
t_critical = qt(.995, n - 1)
lower = xbar - t_critical*s/sqrt(n)
upper = xbar + t_critical*s/sqrt(n)

(answer = c(lower,upper))
## [1] 16.32468 20.47532
  1. The population must be normal.
    1. Not reasonable because it should be a confidence interval not a probability interval.

  1. Reasonable interpretation.

  2. Not reasonable because it should be confidence interval not a population percentage.

  3. Not reasonable because it should be the population parameter of Americans not just Idaho.

  1. We can be 90% confident that the mean Taco Bell drive-thru service time is within 161.5 seconds and 164.7 seconds.

  2. Decrease the level of confidence and increase the sample size.

    1. Because in order to calculate the confidence interval the curve needs to be normally distributed in. By increasing the sample size, the curve becomes more centered. By the CLT, the formula only applies if the population is normal and/or n>30.

  1. The sample size is smaller than 5% of the total population.

  2. (0.1647, 0.1693); we can be 90% confident that the drivers that had a positive BAC in fatal crashes had a mean BAC between 0.1647 and 0.1693 g/dL.

n = 51
xbar = .167
s = .01
t_critical = qt(.95, n - 1)
lower = xbar - t_critical*s/sqrt(n)
upper = xbar + t_critical*s/sqrt(n)

(answer = c(lower,upper))
## [1] 0.1646533 0.1693467
  1. It is possible since the confidence level is not 100%, but it is unlikely that the mean is 0.08 g/dL.
  1. (12.05, 14.75); we can be 99% confident that mean number of books Americans read either all or part of during the preceding year is between 12.05 and 14.75 books.
n = 1006
xbar = 13.4
s = 16.6
t_critical = qt(.995, n - 1)
lower = xbar - t_critical*s/sqrt(n)
upper = xbar + t_critical*s/sqrt(n)

(answer = c(lower,upper))
## [1] 12.04932 14.75068
  1. (1.08, 8.12); we can be 95% confident that the mean incubation period of the SARS virus is between 1.08 and 8.12 days.
n = 81
xbar = 4.6
s = 15.9
t_critical = qt(.975, n - 1)
lower = xbar - t_critical*s/sqrt(n)
upper = xbar + t_critical*s/sqrt(n)

(answer = c(lower,upper))
## [1] 1.084221 8.115779

9.3 5-13 odds

  1. (10.12, 30.14).
n = 20
lower = (small_value = qchisq(.05, n-1))
upper = (large_value = qchisq(.95, n-1))

(answer = c(lower, upper))
## [1] 10.11701 30.14353
  1. (9.54, 40.29).
n = 23
lower = (small_value = qchisq(.01, n-1))
upper = (large_value = qchisq(.99,n-1))

(answer = c(lower, upper))
## [1]  9.542492 40.289360
    1. (7.94, 23.66).
n = 20
ssquared = 12.6
small_value = qchisq(.05, n-1)
large_value = qchisq(.95, n-1)

lower = (n-1)*ssquared/large_value
upper = (n-1)*ssquared/small_value

(answer = c(lower, upper))
## [1]  7.942004 23.663111
  1. (8.59, 20.63); as the sample size increases the width of the interval decreases.
n = 30
ssquared = 12.6
small_value = qchisq(.05, n-1)
large_value = qchisq(.95, n-1)

lower = (n-1)*ssquared/large_value
upper = (n-1)*ssquared/small_value

(answer = c(lower, upper))
## [1]  8.586138 20.634315
  1. (6.61, 31.36); as the level of confidence increases the width of the cofidence interval increases.
n = 20
ssquared = 12.6
small_value = qchisq(.01, n-1)
large_value = qchisq(.99, n-1)

lower = (n-1)*ssquared/large_value
upper = (n-1)*ssquared/small_value

(answer = c(lower, upper))
## [1]  6.614928 31.364926
  1. (1.61, 4.28); we can be 95% confident that the standard deviation prive of a 4 GB flash memory card is between 1.61 and 4.28 dollars.
n = 10
ssquared = (2.343)^2
small_value = qchisq(.025, n-1)
large_value = qchisq(.975, n-1)

lower = (n-1)*ssquared/large_value
upper = (n-1)*ssquared/small_value

(answer = sqrt(c(lower,upper)))
## [1] 1.611598 4.277405
  1. (849.69, 1655.35); we can be 90% that the standard deviation repair cost of a low impact bumper crash on a mini- or micro-car is between 849.69 and 1655.35 dollars.
n = 14
ssquared = (1114.412)^2
small_value = qchisq(.05, n-1)
large_value = qchisq(.95, n-1)

lower = (n-1)*ssquared/large_value
upper = (n-1)*ssquared/small_value

(answer = sqrt(c(lower,upper)))
## [1]  849.6926 1655.3548