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; this interpretation implies that the population mean varies rather than the interval.

  2. Correct

  3. Flawed; this interpretation makes an implication about individuals rather than the mean.

  4. Flawed;the interpretation should be about the mean number of hours worked by adult Americans, not about adults in Idaho.

23. We are 90% confident that the mean drive-through service time of Taco Bell restaurants is between 161.5 and 164.7 seconds.

25. 1.) increase the sample size. 2.) decrease the level of confidence to narrow the confidence interval.

27.

  1. Since the distribution of blood alcohol concentrations is not normally distributed, highly skewed right, the sample must be large so that the distribution of the sample mean will be approximately normal.

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

  3. Lower bound: 0.1647, upper bound: 0.1693. We are 90% confident that the mean BAC in fatal crashes where the driver had a positive BAC is beween 0.1647 and 0.1693 g/dL.

  4. Yes, it is possible that the mean BAC is less than 0.08 g/dL, because it is possible that the true mean is not captured in the confidence interval, but it is not likely.

29. Lower bound: 317.63 licks, upper bound: 394.57 licks. We are 95% confident the mean number of licks to the center of a Tootsie pop is between 317.63 and 394.57.

31.

  1. 4.893

  2. Lower bound: 4.690, upper bound: 5.096. We’re 95% confident the mean pH of rain water in Tucker County, WV 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. Lower bound: 4.607, upper bound: 5.179. We’re 99% confident the mean pH of rain water in Tucker County, WV is between 4.607 and 5.179.

  2. As the level of confidence increases, teh 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 bound: $1035.8, upper bound: $2477.2. We’re 95% confident the mean repair cost for a low impact collision involving mini or micro vehicles is between 1035.8 and 2477.2

  2. The 95% confidence interval would likely be narrower because there is less variability in the data because variability associated with make of the vehicle has been removed.

9.3

5. X^2 0.95 = 10.117, X^2 0.05 = 30.144

7. X^2 0.99 =9.542, X^2 0.01 = 40.289

9.

  1. Lower bound: 7.94, upper bound: 23.66

  2. Lower bound: 8.59, upper bound: 20.63. The width of the interval decreases.

  3. Lower bound: 6.61, upper bound: 31.36. The width of the interval increases.

11. Lower bound: 0.226, upper bound: 0.542. We can be 95% confident that the population standard deviation of the pH of rainwater in Tucker County, WV is between 0.226 and 0.542

13. Lower bound: $734.8, upper bound: $1657.5, we can be 90% confident that the population standard deviation of repair costs of a low-impact bumper crash on a mini or micro car is between $734.8 and $1657.5