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. (16.85,19.95)
  2. (17.12,19.69) Increasing n shortens the interval.
  3. (16.324,20.46) Increasing the confidence increases the margin of error.
  4. This means the population must be normal.

23.

  1. B
  2. Type answer here.
  3. Type answer here.
  4. Type answer here.

25.

We are 90% confident that the drive thru times for Taco Bell is between 161.55 and 164.7 seconds.

27.

Increasing the n or decreasing the confidence level would fix this.

29.

  1. Since its skewed right, there has to be a big n so that the population can be approximately normal.
  2. n has to be less than or equal to 5% of the population
  3. (.1647,.1693)
  4. Yes, because the true mean COULD not be in the interval, though its unlikely.

31.

(12.05, 14.75) We are 99% confident that the mean amount of books read by Americans in the past year was between 12.05 and 24.75

33.

(1.08, 8.12) 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. ? Type answer here. The probability a type I error was made is 5%.
  2. Describe in words what a type II error is in this situation. Type answer here. That’s when we say that the average amount of cholesterol is lowered is not within the interval when it actually is.