9.2

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 to 19.95
  2. 17.12 to 19.68; increased sample size decreases E
  3. 16.32 to 20.48; Increased confidence level increases E
  4. Population must be normal

23.

  1. Flawed - it is not the probability of mean
  2. Reasonable explanation
  3. Flawed - this is not the range of hours worked by all, rather the mean
  4. Flawed - this is a survey of Americans, not Idahoans

25.

90% confident that the mean is between 161.5 and 164.7.

27.

Increase sample size; decrease level of confidence to 90%

29.

  1. BACs are not normally distributed so a large sample size is needed.
  2. The sample is a small portion (less than 5%) of the population.
  3. 90% confident that the mean is between 0.165 to 0.169
  4. Possible but highly unlikely that the true mean is so far outside of the sample calculations

31.

99% confident that mean is between 12.05 and 14.75

33.

95% confident that mean is between 1.08 and 8.12.

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. ? Type I error would mean that you think the new medication is more effective when it is not. Research shows 95% confidence that it is more effective, so probability of type I error is 5%.

  2. Describe in words what a type II error is in this situation. A type II error in this situation would be calculations showing that it didn’t have a larger lowering effect when in fact it did.

9.3

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 you sample standard deviation s = 2 and the sample size = 35, and your confidence level is 95% this is how you can have R calculate a Confidence Interval for \(\sigma\).

conf_sig(s = 2, size = 35, conf = .95)
## [1] 1.617744 2.620404

5

Left critical value: 10.12; Right critical value: 30.14

7

Left critical value: 9.54; Right critical value: 40.29

9

  1. 7.94 to 23.66
  2. 8.59 to 20.63; increasing sample size decreases width of interval
  3. 6.61 to 31.36; increasing level of confidence increases width of interval

11

95% confident standard deviation of the price is between $1.61 and $4.28

13

90% confident the standard deviation repair cost is between $849.7 and $1655.34