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) Increasing the sample size decreases the margin of error
  3. (16.32,20.48) Increasing the level of confidence increases the margin of error
  4. If n=15, the population must be normal

23.

  1. Incorrect; implies that the population mean varies not in the interval
  2. Correct
  3. Incorrect; makes implications about people rather than the mean
  4. Incorrect; the interpretation should be about the mean number of hours worked by adult Americans, not 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.

Increase the sample size and decrease the level of confidence

29.

  1. Since the distribution of blood alcohol concentrations is not normally distributed, the sample must be large so that the distribution of the sample mean will be approximately normal.
  2. The sample size is less than 5% of the population.
  3. (0.1647,0.1693) We are 90% confident that the mean BAC in fatal crashes where the driver 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 in the confidence interval, but it is not likely.

31.

(12.05,14.75) We can be 99% confident that the mean number of books read by Americans in the past year was between 12.05 and 14.75.

33.

(1.08,8.12) We can be 90% 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 or 5%

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

They don’t reject the null hypothesis that the average amount is 10 mg/dL when, in fact, the new medication increases the lowering effect to more than 10 mg/dL.