You can use the following syntax to check your answers. Note the answers you get in R will not be EXACTLY the same you get by hand but they should be pretty close.

If \(\bar{x} = 18.4\), sample standard deviation is 4.5, sample size = 35, and your confidence level is 95% this is how you can have R calculate a Confidence Interval for you.

conf_int(xbar = 18.4, size = 35, conf = .95, s = 4.5)
## [1] 16.8542 19.9458

21.

  1. Lower bound = 103.7, upper bound = 112.3
  2. lower bound = 17.12, upper bound = 19.68, which increases sample size and decreases margin of error
  3. Lower bound = 16.32, upper bound = 20.48, which increases the confidence level and increases margin of error
  4. If n = 15, then the population must be normal

23.

  1. Flawes because the interpretation implies that the ppulation mean varies rather than the interval
  2. Correct
  3. Flawed becuase the interpretation makes a statement about individuals rather than the mean
  4. Flawed, instead the interpretation should be about the mean number of hours worked by adult Americans, and not about adults in Idaho

25.

90% confident that the mean drive-through service time of restaurants is between 161.5 and 164.7 seconds

27.

Increase the sample size, and decrease the level of confidence to narrow the confidence interval

29.

  1. Since the distribution of BAC is not normally distributed, the sample must be large so the distrbution of the sample mean will be approximately normal
  2. The sampe size is less than 5% of the population
  3. Lower bound = .1647, upper bound = .1693, and we are 90% confident that the mean BAC in fatal crashes where the driver had a positive BAC is between .1647 and .1693
  4. Yes it is possible becuase it is possible that the true mean is not captured in the confidence interval

31.

Lower bound = 12.05 books, upper bound = 14.75 books, and we can be 99% confident that the mean read by Americans in the past year was between 12.05 and 14.75

33.

Lower bound = 1.08 days, upper bound = 8.12 days and we can be 95% confident that the mean incubation period of patients with SARS is between 1.08 and 8.13

Question

A current medicine widely available on the market is known to lower cholesterol by an average amount of 10 mg/dl. A new medicine becomes available on the market. The research publication associated with the new medicine displays a 95% Confidence Interval of the average lowering effect to be (14 mg/dl, 23 mg/dl).

  1. In deciding that the new medication is more effective then the old medication what is the Probability you made a type I error. ? .5

  2. Describe in words what a type II error is in this situation. .025