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; UP=19.95
  2. LB= 17.11; UP=19.69; increasing n, decreases E (margin of error)
  3. LB= 16.31; UP= 20.49; increasing the level of confidence, increases E margin of error
  4. if n=15 then the population must be normal to compute a condifence interval

23.

  1. This answer is flawed because says probability of where the mean may lie rather than saying that we are confident where the mean lies; it makes the mean seem variable instead of the interval.
  2. Correct answer
  3. Answer is flawed because it does not mention the mean # of hours worked but rather makes an implication about the individuals
  4. Answer is flawed because it talks about adults only in Idaho when the survey is describing American Adults

25.

we are 90% confident that the mean drive-through service time at Taco Bell is between 161.5 seconds and 164.7 seconds

27.

to increase the precision of the interval, either 1) increase the sample size n or 2) decrease the level of confidence to decrease the margin of error and narrow the interval

29.

  1. a large sample size is needed to construct a confidence interval because then the distribution of the sample mean will be approx. normal
  2. the sample (51) is less than 5% of the population
  3. LB=0.165 UP=0.169; we are 90% confident that the mean BAC in fatal crashes is between 0.165 and 0.169 grams per deciliter
  4. yes, it is possible because it is possible that the true mean BAC is not within the confidence interval but it is very unlikely that this is true.

31.

LB=12.05 UB=14.75 we are 99% confident that the mean number of books that Americans either read all or part of during the preceding year is between 12.05 and 14.75

33.

LB=1.08 UP=8.12 we are 95% confident that the mean incubation period of 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 you made a type I error is 0.05 or a 5% chance.

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

A type II error is failing to reject the null hypothesis when it is false. So, the type II error in this situation would be accepting that that the new medication is not more effective than the old one.