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 incorrect because we are not looking for probability.

  2. This is correct.

  3. Incorrect, we are not producing a statistic for the percentage of adults who worked between the hours.

  4. Incorrect, as adults in Idaho is too specific.

23.

This means that we are 90% confident that the mean drive through service time of Taco Bell restaraunts is between 161.5 and 164.7 seconds.

25.

To increase the precision of the interval, increase the sample size and decrease the confidence level.

27.

  1. Since the distrubution of blood alcohol concentrations is not normally distributed, the sample size 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. t0.05 = 1.676, Lower bound = 0.1647, Upper bound = 0.1693 We are 90% confident that the mean BAC in fatal crashes where the driver had a postive BAC is between 0.1647 and 0.1693.

  4. It is possible that the mean BAC is less than 0.08 because the true mean might not have been captured in the confidence interval.

29.

Lower bound = 317.64, Upper bound = 394.56

We are 90% confident that the mean number of licks is between 317.63 and 394.57

31.

  1. x bar = 4.893

  2. We are 95% confident that hte mean pH is between 4.960 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. We are 99% confident that the mean pH 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. We are 95% confident the mean repair cost for a low-impact collision involving mini and micro vehicles is between 1035.8and 2477.2

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

9.3

5.

x2 0.95 = 10.117, x2 0.05 = 30.144

7.

x2 0.99 = 9.542, x2 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 as the sample size decreases

  1. Lower bound = 6.61, Upper bound = 31.36

The width of the interval increases as the confidence level increases

11.

s2 = 0.102, x2 0.975 = 3.816, x2 0.025 = 21.920 Lower bound = 0.226, Upper bound = 0.542

We can be 95% confident that the population standard deviation is between 0.226 and 0.542

13.

s2 = 1,014,963,9651, x2 0.95 = 3.325, x2 0.05 = 16.919

Lower bound = 734.8, Upper bound = 1657.5

We are 90% confident that the population standard deviation is between 734.8 and 1657.5.