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 an ureasonable interpretation because the varience is talking about the population mean instead of the interval.

  2. This is a reasonable interpretation.

  3. This is an ureasonable interpretation because it interprets the 95% in terms of the individuals instead of referring to the mean.

  4. This is an ureasonable interpretation because the information provided is about adult Americans, not adults in Idaho.

23.

We are 90% confident that the mean drive-through service time for Taco Bell was between 161.5 seconds and 164.7 seconds.

25.

One recommendation for increasing the precision of the interval is to survey more individuals (increaes the sample size). Another recommendation is to decreae the confidnce level.

27.

  1. A large sample size is needed in order to make the data appear more normally distributed.

  2. The requirements for construction a confidence interval are satisfied because the sample size is less than 5% of the entire pooulation.

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

  4. Yes it is possible that the mean BAC of all drivers involved in fatal accidents who are found to have positive BAC values is less than the legal intoxication level because the true mean may not be seen in the confidence interval. Although it is possible, it still is not likely.

29.

We are 95% confident that the mean number of licks required to get to the center of a Tootsie Pop was between 317.63 and 394.57 licks. The lower bound is 317.63 and the upper bound is 394.57.

31.

  1. 4.893

  2. We are 95% confident that the mean pH of rainwater in Tucker County was between 4.69 and 5.096. The lower bound is 4.69 and the upper bound is 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 was between 4.607 and 5.179. The lower bound is 4.607 and the upper bound is 5.179.

  2. As the level of confidence increases, the margain of error increases. This makes sense because you would be adding/ subtracting more from the point estimate.

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. We are 95% confident that the mean cost of repair for the population mean was between 1035.8 and 2477.2 dollars. The lower bound is 1035.8 and the upper bound is 2477.2.

  2. A 95% confidence interval would be narrower because since there is only one type of car being measured, the variance in the data will be less.

9.3

5.

10.117 and 30.144

7.

9.542 and 40.289

9.

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

  2. The lower bound is 8.59 and the upper bound is 20.63. Increasing the sample size decreases the width of the interval.

  3. The lower bound is 6.61 and the upper bound is 31.36. Increasing the level of confidence increases the width of the interval.

11.

We are 95% confident that the the standard deviation pH of rain water in Tucker County was between 0.226 and 0.542. The lower bound is 0.226 and the upper bound is 0.542.

13.

We are 90% confident that the the standard deviation repair cost of a low impact collision involving mini and micro vehiclesx was between 734.8 and 1657.5 dollars. The lower bound is 734.8 and the upper bound is 1657.5.