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. 17.11, 19.69; the margin of error decreases slightly
  3. 16.32, 20.48; the margin of error increases slightly
  4. The population must be normally distributed.

23.

  1. We are 95% confident, which is not a representation of the probability.
  2. true
  3. We are 95% sure that this is true, this statement is a blanket 100%.
  4. The calculated confidence interval is for the entire US, so the numbers in Idaho should represent only 2% of the total data being used. To get a confidence interval for work hours in Idaho, you would have to conduct a survey where all the results came from there.

25.

We are 90% confident that the average time it takes to go through a Taco Bell drive-through is between 161.5 seconds and 164.7 seconds.

27.

Increase the sample size, or lower the confidence level.

29.

  1. Because if the data is not normally distributed the sample size has to be relatively large to construct a confidence interval from it.
  2. The sample size is less than 5% of the total population.
  3. .1647, .1693
  4. Yes, but it is extremely unlikely, especially considering how much higher than that all the data suggests it probably is.

31.

We are 99% confident that the mean number of books Americans read all or part of each year is between 12.05 and 14.75. (I used 1000 degrees of freedom because the difference between 100 and 1000 looked quite small, so I figured the difference between 1000 and 1005 would be negligible and I’m not sure how to find the value with 1005 degrees of freedom).

33.

We are 95% confident that the mean incubation period for the SARS virus 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. ? .05: the alpha value represents the probability of a type I error.

  2. Describe in words what a type II error is in this situation. A type II error in this case would mean that someone decides the medication really does lower the cholesterol by an amount that falls within the confidence interval, while in reality it does not.