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. n-1=34 D.F.;Lower Bound: 16.85; Upper Bound = 19.95
  2. n= 50; Lower Bound: 17.12; Upper Bound: 19.68 - Increasing sample size will decrease the M.E.
  3. n=35; Lower Bound: 16.32; Upper Bound: 20.48 - Increasing the level of confidence will increase the M.E.
  4. The population must be normal if n=15

23.

  1. incorrect - this interpretation implies populatuon mean instead of the interval.
  2. Correct
  3. Incorrrect - This interpetation makes an implication about the individual instead of the mean
  4. Incorrect - This interpretation makes reference to adults in Idaho only instead of Americans adults.

25.

We’re 90% confident that the mean of taco bell drive-thru services is between 161.5 and 164.7

27.

Increase the sample size and decrease level of confidence to narrow the confident interval

29.

  1. The distribution is skewed right, not normal according to the text; we’ll need a larger sample size for the distribution to be approximately normal
  2. The sample size is less than 5% of the population
  3. Lower Bound: 0.1647; Upper Bound: 0.1693 - We’re 90% confident that the BAC mean in fatal crashes where a driver had a positive BAC is between 0.1647 and 0.1693
  4. Yes, it’s possible because the true mean might not be captured in the confident interval, but it’s not likely.

31.

n-1 = 1005 D.F.; Lower Bound: 12.05; Upper Bound: 14.75 - We’re 99% confident that the mean numbers of books that American read either all or part of during the past year was between 12.05 and 14.75

33.

n-1 = 80 D.F. - Lower Bound: 1.08; Upper Bound: 8.12 - We’re 95% confident that the mean incubation period of SARS virus 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. ? 1; type I error is made if evidence leads the researcher to believe the new medicine will lower cholesterol by an average of 14 mg/dl and 23mg/dl(he rejects the null hypothesis) when, in facr, the new medicine does not lower cholesterol between 14mg/dl and 23mg/dl

  2. Describe in words what a type II error is in this situation. *Type II error is made if the researcher does not reject the null hypothesis that the new available medicine lower cholesterol by 10mg/dl when, in fact the new medicine does lower cholesterol by more then 10mg/dl

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 n-1 = 19 D.F. 10.117 AND 30.144

7 n-1 = 22 D.F. 9.542 AND 40.289

9

  1. n = 19 d.f. - Lower Bound: 7.94; Upper Bound: 23.66
  2. n-1=29 D.F.Lower Bound:8.59; Upper Bound:20.63 - Increasing the sample size decreases the width of the interval
  3. n-1 = 19 D.F. - Lower Bound: 6.61; Upper Bound: 31.36 - Increasing the level of confidence increases the width of the interval

11

n-1= 9+D.F.; Lower Bound: 1.612; Upper Bound: 18.3 We can be 95% Confident that the population standard deviation of the 4GB prices at online retailers is between 1.612 and 4.278

13

Lower Bound: 849.7; Upper Bound: 1655.3 - We can be 90% confident that the population standard deviation of repair costs of a low-impact bumber is between 849.7 and 1655.33