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 not a reasonable interpretation, since probability is not the same thing as confidence.

  2. This is a reasonable assumption.

  3. This is not a reasonable assumption since confidence interval do not indicate anything about the whole population.

  4. This is not a reasonable assumption since it is restricting the confidence interval to a specific sample in Idaho.

23.

We are 90% confident that the mean amount of service time in the drive-throughs of fast-food restaurants is between 161.5 seconds and 164.7 seconds.

25.

We can either: (1) increase the sample size, or (2) increase the confidence interval.

27.

  1. Because the data here is highly skewed right, we need a huge sample size in order to make sure that the t-distribution is shaped normally.

  2. The number of fatal crashes in which the driver had a positive BAC is definitely lower than the population of entire crashes, thus, a confidence interval can be constructed.

  3. 90% C.I = (.165, .169).

  4. No it is not possible, since the 90% confidence interval suggests that there is a 90% confidence that the mean BAC is between .165 and .167, which is well over the legal limit of .08.

29.

95% C.I = (317.63, 394.57). We are 95% confident that the mean number of licks it takes to get to the center of a Tootsie Pop is between 317.63 and 394.57 licks.

31.

  1. x-bar = 4.89.

  2. 95% C.I = (4.69, 5.09). We are 95% confident that the mean pH of rain is between 4.69 and 5.09.

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. 99% C.I = (4.60, 5.18). We are 99% confident that the mean pH of rain is between 4.60 and 5.18.

  2. The interval gets bigger as the confidence increases. This makes sense because a higher confidence would have to include a greater value of possible means in order to ensure the high confidence.

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. 95% C.I = (1035.86, 2477.14). We are 95% confident that the mean cost of repairing a low-impact collision is between 1035.86 and 2477.14 dollars.

  2. The 95% confidence interval would be narrower, since the sample size is pretty small.

9.3

5.

10.117, 30.144.

7.

9.542, 40.289.

9.

  1. 90% C.I = (7.94, 23.66).

  2. 90% C.I = (8.59, 20.63). The width of the interval decreases as the sample size gets bigger.

  3. 98% C.I = (6.61, 31.36). Increasing the confidence increases the width of the interval.

11.

95% C.I = (.23, .54). We are 95% confident that the standard deviation of the pH of rain is between .23 and .54.

13.

90% C.I = (734.78, 1657.49). We are 90% confident that the standard deviation cost of repairing a low-impact collision is between $734.78 and $1657.49.