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. Reasonable

  2. Reasonable

  3. Not reasonable. The proportion is about the probability that the mean lies within the range.

  4. Not reasonable. The interval is only relevant to the population studied.

23.

They are 90% confident that the mean drive-thru service time for Taco Bell lies between 161.5 and 164.7 seconds.

25.

To increase the precision of the range, lower the confidence interval or increase the sample size.

27.

  1. A large sample size increases the precision of a study.

  2. The study used simple random sampling and is a normal distribution

  3. 0.1647 to 0.1693

  4. It is possible but unlikely that the mean is less than 0.08.

29.

317.63 to 394.57

31.

  1. xbar=4.893

  2. 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. 4.607 and 5.179

  2. ME increases as CI 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. 1035.8 and 2477.2

  2. Less variability leads to a smaller CI

9.3

5.

Xsquared0.95=10.117 Xsquared0.05=30.144

7.

Xsquared0.99=9.542 Xsquared0.01=40.289

9.

  1. 7.94 and 23.66

  2. 8.59 and 20.63

  3. 6.61 and 31.36

11.

0.226 and 0.542

13.

734.8 and 1657.5