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. This is flawed because it implies that the population mean varies instead of the interval.

  2. This is a reasonable interpretation.

  3. This is flawed because it makes an implication about individuals instead of the mean.

  4. This is flawed because it is about adults in Idaho instead of the mean number of hours adult Americans worked.

23.

This means that we are 90% confident that the mean drive-through time of Taco Bells is between 161.5 and 164.7 seconds.

25.

You can increase the sample size or decrease the level of confidence.

27.

  1. Since the distribution of blood alchohol concentrations is right skewed the sample must be so large that the distribution of the sample mean will be approximately normal.

  2. Becasue the sample size is 5% less than the population.

  3. The lower bound is 0.1647 while the upper bound is 0.1693. We are 90% confident that the mean BAC in fatal crashes when the driver had a positive BAC is between 0.1647 and 0.1693 g/dL.

  4. Yes because it is possible that the true mean is not captured in the confidence interval.

29.

The lower bound is 317.63 licks while the upper bound is 394.57 licks. We are 95% confident the mean number of licks is between 317.63 and 394.57.

31.

  1. 4.893

  2. The lower bound is 4.690 while the upper bound is 5.096. We are 95% confident the mean pH of rain water is between 4.690 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. The lower bound is 4.607 while the upper bound is 5.179. We are 99% confident the mean pH of rain water is between 4.607 and 5.179.

  2. As the level of confidence increases the margin of error increases.

33.

  1. skip

  2. skip

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

  1. The lower bound is 1035.8 dollars while the upper bound is 2477.2 dollars. We are 95% confident the mean repair cost is between 1035.8 dollars and 2477.2 dollars.

  2. The interval would become narrower because variability associated with the make of the car would be removed.

9.3

5.

10.117, 30.144

7.

9.542, 40.289

9.

  1. The lower bound is 7.94 while the upper bound is 23.66.

  2. The lower bound is 8.59 while the upper bound is 20.63. The width of the interval decreases.

  3. The lower bound is 6.61 while the upper bound is 31.36. The width of the interval increases.

11.

The lower bound is 0.226 while the upper bound is 0.542. We are 95% confident the population standard deviation of the pH of rainwater is between 0.226 and 0.542.

13.

The lower bound is 734.8 dollars while the upper bound is 1657.5 dollars. We are 90% confident the population standard deviation of repair costs is between 734.8 dollars and 1657.5 dollars.