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. lower: 16.85 upper: 19:95
  2. lower: 17.12 upper: 19.68 when the sample size increases, the margin of error decreases
  3. lower : 16.32 upper:20.48 when the confidence level increases, the margin of error increases
  4. if n = 15 population must be normal

23.

  1. flawed because it’s basically saying that the mean varies instead of the interval
  2. correct
  3. flaed because the interpretation talks about the individuals rather than the mean
  4. flawed because it talks about the mean number of hours worked by all americans rather than just americans from idaho.

25.

we are 90% confident that the mean drive through service time of taco Bell restaurants between161.5 and 164.7 seconds

27.

increase the sample size and lower the level of confidence

29.

  1. the distribution of blood alchohol concentration is skewed to the right. the sample size must be enlarged until the sample size is normal.
  2. the sample size is less than 5%
  3. lower : 0.1647 upper 0.1693 we are 90% confidentthat the true mean bloodalchohol concentration in fatal car crasherswhere the driverhad a postive blood alchol concentration is between 0.1647 and 0.1693
  4. yea it is possible that the mean bac is less than 0.08 because it is a possibilitythat the true mean is not captured in the confidence interval. however, itis not likely.

31.

lower: 12.05 upper: 14.75 we are 99% confident that the mean numberof books read by americans in the past year is between 12.05 and 14.75

33.

lower 1.08 upper 8.12 we are 95% confident that the mean incubation period for 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. ? the probability of a type 1 error is 0.05 or 5%.

  2. Describe in words what a type II error is in this situation. a type 2 error would indicate that the new medicine has no lowering effect on cholesterol, when in fact it does.