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. (17.12,19.68)
  3. (16.32,20.48)
  4. For a small sample (n = 15 < 30), the population must be normally distributed.

23.

  1. wrong, it indicates that the population mean varies rather than the interval.
  2. correct
  3. wrong, it makes an implication about individuals rather than the mean.
  4. wrong, it should be about the mean number of hours worked by adult Americans, not about 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.

  1. Increase the sample size
  2. decrease the level of confidence

29.

  1. Since the distribution is highly skewed right, the sample must be large in order to make the distribution of the sample mean approximately normal.
  2. The sample is less than 5% of the population.
  3. （0.1647，0.1693）
  4. Yes， it is possible that the true mean is not captured in the confidence interval.

31.

(12.05,14.75) We are 99% confident that the population mean number of books read by Americans during 2005 was between 12.05 and 14.75 books.

33.

(1.08,8.12) We are 95% confident that the population 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. ? 5%

  2. Describe in words what a type II error is in this situation. They say this medicine lowers cholesterol by how much the CI is more than 10 mg/dL, but truth is that it doesn’t.