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. The statement is flawed, it implies that the population mean varies rather than the interval.

  2. This statement is correct because an interval has been provided for the population mean.

  3. THis statement is flawed, the interpretation makes an implication about the individuals rather than the mean.

  4. Statement is flawed, because 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 restaraunts is between 161.5 and 164.7 seconds.

25.

Increase the sample size and decrease the confidence level to narrow the confidence interval.

27.

  1. Sample size must be large so that the distribution of the sample mean will be approximately normal.

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

  3. t0.05 = 1.676 LB = .1647 UB = .1693

We are 90% confident that the mean BAC in fatal crashes where the drover has a postive BAC is between .1647 and .1693.

  1. It is possible that the mean BAC is less than 0.08 g/dl because it’s possible that the true mean is not captured in the confidence interval, but it is not likely.

29. t0.025 = 1.987

LB = 317.63 UB = 394.57

31.

  1. 4.893

  2. s = .319 t0.025 = 2.201 LB = 4.69 UB = 5.096 We are 95 % confident that the mean ph of water in TC, WV is between 4.69 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 = 4607 UB = 5.197 We are 99% confident that the mean pH of rain water in TC, WV is between 4.607 and 5.179

  2. 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. xhat = 1756.5 s = 1007.5 t0.0025 = 2.262 LB = 1035.8 UB = 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 confidence interval would likely be narrower because there is less variability in the data because variability is associated with the make of the vehicle has been removed.

9.3

5.

x^2 .95 = 10.117 x^2 0.05 = 30.144

7.

x^2 0.99 = 9.542 x^2 0.01 = 40.289

9.

  1. x^2 .95 =10.117, X^2 .05 = 30.144 LB = 7.94 UB = 23.66

  2. X^2 0.95 = 17.708 X^2 .05 = 42.557 LB=8.59 UB=20.63 Width of the interval increases as the confidence level increases.

  3. X^2 0.99 = 7.633 X^2 .01 = 36.191

LB = 6.61 Ub = 31.36

Width of the interval increases as the confidence level increases.

11.

s^2 = .102, X^2 0.975 =3.816, X^2 .025 = 21.920

LB = .226 UB = .542

We can be 95% confident that the population standard deviation of the pH of rainwater in TC, WV is between 0.226 and 0.542.

13.

s^2 = 1,014,963.9651 x^2 0.95 = 3.325 x^2 0.05c= 16.919

LB = 734.8 UB = 1657.5

We are 90% confident that the population SD of repair costs is of a low impact bumper crash on a mino or micro car is between $734.8 and $1657.5.