9.2

21

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(16.86,19.94))
## [1] 16.86 19.94
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(17.12,19.68))
## [1] 17.12 19.68
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(16.32,20.48))
## [1] 16.32 20.48

It appears the margin of error increases.

  1. The population must be normal.

23

  1. A confidence interval is NOT a probability interval.

  2. Correct

  3. A confidence interval is NOT a census.

  4. We are making a statement about the population parameter of the whole country, NOT just Idaho.

25

This meants that the QSR is 90% confident that the true mean drive-through time of Taco Bell’s customers is between 161.5 seconds and 164.7 seconds

27

  1. conduct a larger survey with a bigger n to account for sampling variability 2)conduct the problem at a higher confidence level (example, 99.9% confidence)

29

  1. the larger the sample size, the more accurate the results will be because it accounts for sampling variability

  2. 25,000>30, SRS allows for no-bias and complete randomness of subjects

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(.143,.1694))
## [1] 0.1430 0.1694
  1. It is possible because while we are 90% confident, it is still not 100% proven that the true mean falls in this level

31

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(12.05,14.75))
## [1] 12.05 14.75

I am 99% confident that the true mean number of books read by Americans falls between 12.05 books and 14.75 books.

33

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(1.08,8.12))
## [1] 1.08 8.12

I am 95% confident that the truemean incubation period of SARS patients falls between 1.08 days and 8.12 days.

9.3

5

n = 20
(small_value = qchisq(.05, n-1))
## [1] 10.11701
(large_value = qchisq(.95, n-1))
## [1] 30.14353

7

n = 23
(small_value = qchisq(.01, n-1))
## [1] 9.542492
(large_value = qchisq(.99, n-1))
## [1] 40.28936

9

  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(7.94,23.66))
## [1]  7.94 23.66
  1. (8.59, 20.63), width 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(8.59,20.63))
## [1]  8.59 20.63

width decreases

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(6.61,31.36))
## [1]  6.61 31.36

width increases

11

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(1.612,4.278)))
## [1] 1.269646 2.068333

I am 95 % confident that the true population standard deviation of the prices of 4GB flash memory cards at online retailers is between 1.612 dollars and 4.278 dollars

13

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(849.7,1655.3)))
## [1] 29.14961 40.68538

I am 90% confident that the true population standard deviation of repair costs of a low-impact bumper crash on a mini/microcar is between 849.7 and 1655.3 dollars