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. LB - 16.85 UB - 112.3
  2. LB - 17.12 UB - 19.68
  3. LB - 16.32 UB - 20.48
  4. The population must be normal.

23.

  1. Wrong. The mean of the population is unchanging.
  2. Right
  3. Wrong. The mean should be the subject of the interpretation, not an individual.
  4. Wrong. The mean should be about the number of hours worked rather than the adults themselves.

25.

90% confident that the service time is between 161.5 and 164.7 seconds.

27.

Sample size with increase and the level of confidence will decrease.

29.

  1. The sample must have been so large that the sample mean results in being normal.
  2. Sample size is 5% or less of the population.
  3. LB - 0.1647 UB - 0.1693. There is a 90% confidence level that the mean is between these bounds.
  4. Yes it is possible, although it is very unlikely to be so.

31.

LB - 12.05 UB - 14.75. There is a 99% confidence that the mean number of books that were read were between these bounds.

33.

LB - 1.08 UB - 8.12. There is a 95% confidence that the mean incubation period was between these bounds.

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. ? The probability of a type one error is 0.05.

  2. Describe in words what a type II error is in this situation. A type two error is assuming the null hypothesis is true when in reality it is not. This means that we accept the medicine to reduce cholesterol by 10mg/dl, when in reality, it doesn’t.