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 lowers 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 instead of the interval
  2. Correct
  3. Flawed, this interpretation makes an implication bour individuals instead of the mean
  4. Flawed, the interpretation should be about the mean number of hours worked by adult Americans not about the adults in Idaho

25.

We are 90% confident that the mean drive through service time of Taco Bell restaurants is between 161.5 and 164.7 seconds

27.

Decrease the level of confidence to narrow the confidence interval and also increase the sample size

29.

  1. Since the distribution is not normally distributed the sample must be large so that the distrubution of the sample mean will be normal
  2. Sample size is less than 5% of the population
  3. Lower bound: 0.1647, upper bound: 0.1693, we are 90% confident that the mean BAC is between 0.1647 and 0.1693 g/dL
  4. Type answer here.

31.

Lower bound: 12.05 books, upper bound: 14.75 books, we are 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, we are 95% confident that the mean incubation period of patients with SARS is between 1.08 and 8.12 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. ?

0.05 probability

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

In this case a type 2 error is if the statement that the new medicine is better is false and we failed to reject it. For example if we didn’t have a large enough sample size when testing our hypothesis.