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. (16.854, 19.946)
  2. (17.121, 19.679). Increasing the sample size decreases the margin of error.
  3. (16.325, 20.475). 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 interpretation implies indivaduals rather than the mean.
  4. Flawed. This interpretation hsould be about the mean number of hours worked by adult Americans not about adults in Idaho.

25.

We are 90% confident that the mean number of drive-through service times of fast-food restaurants in Taco Bell’s was between 161.5 seconds and 164.7 seconds.

27.

  1. increase the sample size.
  2. decrease the level of confidence to narrow the confidence interval.

29.

  1. Since the distribution of blood alcohol concentrations is not normally distributed, because it is highly skewed right, 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. (0.1646, 0.1693). We are 90% confident that the mean BAC in fatal crashes where the driver had a positive BAC is between 0.1646 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’s not likely.

31.

(12.052, 14.748). We are 99% confident that the mean number of books read by Americans in the past year was between 12.052 and 14.748.

33.

(1.084, 8.116). Weare 95% confident that the mean incubation period of patients with SARS is between 1.084 and 8.116 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. ? We say the new medication is more effective than the old medication, truth is it is not.

  2. Describe in words what a type II error is in this situation. We say the new medication is not more effective, but truth is it is more effective.