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. flawed, because this implies that the population mean varies instead of the interval

  2. correct

  3. flawed, because this implies information about individuals instead of the mean

  4. flawed, because this should be related to the mean hours of all adults in America, not just Idaho

23.

90% confidence that the mean service time at Taco Bell drive-throughs is between 161.5 and 164.7 seconds

25.

the sample size could be increased and the level of confidence could be decreased

27.

  1. the distribution of blood alcohol concentrations is skewed right, therefore the the sample has to be large so the sample mean’s distribution is normal

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

  3. lower: 0.165, upper: 0.169, this means that there is 90% confidence that the mean BAC in crashes where the driver had a positive BAC was between 0.165 and 0.169 g/dL

  4. yes, it’s possible that the mean BAC is less than 0.08 g/dL since the true mean may not be captured

29.

lower: 317.6, upper: 394.6, with 95% confidence that the mean number of licks is between 317.6 and 394.6

31.

  1. 4.89

  2. lower: 4.7, upper: 5.1, with 95% confidence that the average pH of rain water is between 4.7 and 5.1

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. lower: 4.61, upper: 5.18, with 99% confidence that the average pH of rain water is between 4.61 and 5.18

  2. as level of confidence increases, margin of error also 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. lower: 1035.8, upper: 2477.2, with 95% confidence that the mean repair cost for a low-impact collision is between $1035.80 and $2477.20

  2. the 95% confidence interval would likely be narrower due to less variablility in the data and the removal of the make of the vehicle

9.3

5.

x^2 0.95=10.12 and x^2 0.05=30.14

7.

x^2 0.99=9.54 and x^2 0.01=40.29

9.

  1. lower: 7.94, upper: 23.67

  2. lower: 8.59, upper: 20.63, the width decreases

  3. lower: 6.61, upper: 31.36, the width increases

11.

lower: 0.226, upper: 0.543, with 95% confidence that the the population STDEV of the pH of rainwater is between 0.226 and 0.543

13.

lower: 734.8, upper: 1657.5, with 90% confidence that the population STDEV of repair costs for a low-impact crash is between $734.80 and $1657.50