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 bound = 16.85; Upper bound = 19.95
  2. Lower bound = 17.12; Upper bound = 19.68; Increasing the sample size will decrease the margin of error.
  3. Lower bound = 16.32; Upper bound = 20.48; Increasing the confidence level will increase the margin of error.
  4. If the sample size/n = 15, then the population must be normal.

23.

  1. Flawed; this interpretation states that the population mean varies instead of the interval.
  2. Correct; this refers to the confidence interval
  3. Flawed; this statement refers to individuals as opposed to the mean.
  4. Flawed; this statement is only about adults in Idaho when it is supposed to be about the mean number of hours worked by adult Americans.

25.

We are 90% confident after examining a sample of 607 customers that the mean drive-through service time of Taco Bell restaurants is between 161.5 seconds and 164.7 seconds.

27.

  1. Increase the sample size
  2. Decrease confidence level in order to narrow the confidence interval

29.

  1. The distribution of blood alcohol concentrations is highly skewed right, so it is not normally distributed. Therefore, the sample must be larger in order for the distribution of sample mean to be normal.
  2. The sample size is less than 5% of the population, so it satisfies the requirements for the confidence interval.
  3. Lower bound = 0.1647; Upper bound = 0.1693; We are 90% confident that the mean BAC of fatal crashes in which the driver had a positive BAC is between 0.1647 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 the true mean is not captured in the confidence interval. This is not likely though.

31.

Lower bound = 12.05 books; Upper bound = 14.75 books; We are 99% confident that the mean number of books Americans read in the past year is between 12.05 and 14.75.

33.

Lower bound = 1.08 days; Upper bound = 8.12 days; We are 95% confident that the mean incubation period of patients with SARS based on the sample 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. ? ** There is a low probability that we made a type I error since alpha equals 0.05. **

  2. Describe in words what a type II error is in this situation. ** A type II error in this situation means that we do not reject the hypothesis that the new medicine will lower cholesterol more than the old medicine when in truth this hypothesis is actually false. **