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: 16.85, Upper Bound: 19.95
  2. Lower Bound: 17.12, Upper Bound: 19.68; increasing the sample size decreases the margin of error.
  3. Lower Bound: 16.32, Upper Bound: 20.48 increasing the level of confidence increases the margin of error.
  4. If n=15, the population must be normal.

23.

  1. Flawed; this interpretation implies that the population mean varies rather than the interval.
  2. Correct.
  3. Flawed; this interpretaton makes an implication about individuals rather than the mean.
  4. Flawed; the interpretation should be about the mean number of hours worked by adult Americans, not about adults in Idaho.

25.

90% confident that the mean drive-through service time of Taco Bell restaurants in between 161.5 anad 164.7 seconds.

27.

  1. Increase the sample size, and 2) Decrease the level of confidence to narrow the confidence interval.

29.

  1. Since the distribution of blood alcohol concentrations is not normally distributed (highly skewed right), the sample must be large so that the distribute of the sample mena will be approximately normal.
  2. The sample size is less than 5% of the population.
  3. Lower Bound: 0.1647, Upper Bound: 0.1693; 90% confidence that the mean BAC in fatal crashes where the dirver had a positive BAC is between 0.1647 and 0.1693 g/dL.
  4. Yes; it is possible that the mean BAC is less than 0.08 g/dL, because it is possible that the true mean is not captured in the confidence interval, but it is not likely.

31.

Lower Bound: 12.05 books, Upper Bound: 14.75 books; 99% confident that the mean number of books 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; 95% confident that the mean incubation period of patients with SARS is between 1.08 and 8.13 days.

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. ? Probability that a type I error was made is 5%.

  2. Describe in words what a type II error is in this situation. A type II error would imply that new medicine doesn’t lower cholesterol more than the old medication, although it does.