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 has flaw because it implies that the population mean varies rather than interval.

  2. This is reasonalbe.

  3. This has flaw because it implies the individuals rather than the mean.

  4. This has flaw because it should be about the mean number of hours worked by adult Americans but 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.

Increase the sample size and decrease the confidence level.

27.

  1. Because the distribution of blood alcohol concentrations is not normally distributed, the sample size needs to be large so that the distribution of the sample mean will be about normal.

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

  3. t0.05=1.676 LB: 0.167-1.676 x 0.010/√51=0.1647 UB: 0.167+1.676 x 0.010/√51=0.1693 We are 90% confident that the mean BAC in fatal crashes where the driver had a positive BAC is between 0.1647 and 0.1693.

  4. It is possible because the true mean is not captured in the confidence interval.

29.

t0.025=1.987 LB: 356.1-1.987 x 185.7/√92=317.63 UB: 356.1+1.987 x 185.7/√92=394.57 We are 95% confident that the number of licks required to reach the candy center of a Tootsie pop is between 317.63 and 394.57.

31.

  1. x=58.71/12=4.893

  2. s=0.319, t0.025=2.201 LB:4.893-2.201 x 0.319/√12=4.690 UB:4.893+2.201 x 0.319/√12=5.096 We are 95% confident that the mean pH of rain water in Tucker County, West Virginia 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. t0.005=3.106 LB:4.893-3.106 x 0.319/√12=4.607 UB:4.893+3.106 x 0.319/√12=5.179 We are 99% confident that the mean pH of rain water in Tucker County, West Virginia is between 4.607 and 5.179.

  2. The margin of error increases as the confidence level 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. x=17565/10=1756.5, s=1007.5, t0.025=2.262 LB: 1756.5-2.262 x 1007.5/√10=1035.8 UB: 1756.5+2.262 x 1007.5/√10=2477.2 We are 95% confident the mean repair cost for a low-impact collision involving mini- and micro-vehicles is between 1035.8 and 2477.2

  2. The interval would be narrower because there’s less variability in the data and the variability associated with the make of the vehicle has been removed.

9.3

5.

x0.95^2=10.117, x0.05^2=30.144

7.

x0.99^2=9.542, x0.01^2=40.289

9.

  1. x0.95^2=10.117, x0.05^2=30.144 LB: (20-1)(12.6)/30.144=7.94 UB: (20-1)(12.6)/10.117=23.66

  2. x0.95^2=17.708, x0.05^2=42.557 LB: (30-1)(12.6)/42.557=8.59 UB: (30-1)(12.6)/17.708=20.63 The width of the interval decresase as the sample size increases

  3. x0.99^2=7.633, x0.01^2=36.191 LB: (20-1)(12.6)/36.191=6.61 UB: (20-1)(12.6)/7.633=31.36 The width of the interval increases as the confidence level increases

11.

s^2=0.102, x0.975^2=3.816, x0.025^2=21.92 LB:√(12-1)(0.102)/21.92=0.226 UB:√(12-1)(0.102)/3.816=0.542 We can be 95% confident that the standard deviation pH of rainwater in Tucker County, West Virginia is between 0.226 and 0.542

13.

s^2=1014963.9651, x0.95^2=3.325, x0.05^2=16.919 LB:√(10-1)(1014963.9651)/16.919=734.8 UB:√(10-1)(1014963.9651)/3.325=1657.5 We are 90% confident that the standard deviation repair cost of a low-impact collision involving mini- and micro-vehicles is between 734.8 and 1657.5