Note in 31 and 33 there are some tedious calculations that I did for you. You can see the output once you knit this file.

9.2

21.

  1. False; confidence refers to the interval, not the population mean.

  2. True.

  3. False; the statement is talking about the individuals rather than the mean.

  4. False; not just talking about adults from Idaho, but adults in America as a whole

23.

We are 90% confident that Taco Bell has an average drive-through service of between 161.5 seconds and 164.7 seconds.

25.

To increase the precision of the interval, decrease the confidence or increase the sample size.

27.

  1. A large sample size is needed to make the data normal.

  2. The sample size is less than 5% of the population.

  3. (0.165,0.169)

  4. It is possible that the true mean was not captured in the interval, but it is not likely.

29.

  1. We are 95% confident that it takes between 317.64 and 394.56 licks to get to the center of a tootsie pop.

31.

  1. 4.893

  2. We are 95% confident that the mean pH of rainwater in Tucker County, WV is between 4.607 and 5.096.

data <- c(4.58,5.72,5.19,4.75,5.05,5.02,4.8,4.74,4.77,4.76,4.77,4.56)
mean(data)
## [1] 4.8925
sd(data)
## [1] 0.3194064

  1. We are 99% confident that the mean pH of rainwater in Tucker County, WV is bewteen 4.607 and 5.179.

  2. As our confidence increase, our interval increases as well 33.

  3. skip

  4. skip

data2 <- c(3148,2057,1758,663,1071,2637,3345,773,743,1370)
mean(data2)
## [1] 1756.5
sd(data2)
## [1] 1007.454

  1. We are 95% confident that the mean repair cost for a low-impact collision involving a mini- or a micro-car would be between $1035.80 and $2477.20.

  2. The confidence would be narrower because the varability associated with the make of the car has been removed.

9.3

5.

10.117, 30.144

7.

9.542, 40.289

9.

  1. (7.94, 23.66)

  2. (8.59, 20.63), increasing the sample size decreases the length of the interval.

  3. (6.61, 31.36), increasing the confidence increases the length of the interval.

11.

We are 90% confident that the population standard deviation of the pH of rainwater in Tucker County, WV is between 0.226 and 0.546

13.

We are 90% confident that the population standard deviation of repair costs of low-impact bumper crash on a mini- or micro-car is between $734.80 and $1657.50.