Question

1) The weekly oral dose of anabolic steroids was measured on a sample of 20 body builders. A 95% confidence interval estimatefortheaverageweeklyoraldoseofanabolicsteroidsobtainedfromtheseresultswas152mgto194 mg. (The margin of error is 21 mg.) Identify which one of the following interpretations is correct.

1. a) 95% of all body builders use between 152 mg and 194 mg of anabolic steroids per week.

2. b) There is a 0.95 probability that the average weekly dose of anabolic steroids used by body builders is between

   152 mgand194mg.

3. c) We are 95% sure that the average weekly dose of anabolic steroids used by body builders is between 152 mg and

   194 mg.

4. d) 94% of the time, the average weekly dose of anabolic steroids used by body builders is between 152 mg and 194 mg.

5. e) We are 95% confident that the average weekly dose of anabolic steroids used by the 20 body builders is between

152 mgand194mg.
f) There is a 95% chance that the weekly dose of anabolic steroid use by body builders is between 152 mg and 194

2) 95% confidence used in question (1) means that

1. a) the confidence interval procedure used in the above example gives intervals that contain the true mean 95% of

   the time.

2. b) the probability that the parameter value is between 152 mg and 194 mg is 0.95.

3. c) 95% of the time, we will get the true mean value in the confidence interval (152 mg, 194 mg).

4. d) the chances of getting a sample statistic in the confidence interval (152 mg, 194 mg) are 95%.

5. e) 95% of the weekly dosages of anabolic steroids used by body builders is in the interval (152 mg, 194 mg).

mg.

3) Margin of error 21 mg used in question (1) can be interpreted as
a) 95% of the time, 173 will differ from the true average weekly oral dose by 21 mg.
b) the mean of 173 mg could actually vary from 152 mg to as high as 194 mg.
c) 95% of the sample means from all possible samples of size 20 will differ from the true average weekly oral dose

by no more than 21 mg.
d) 95% of the time, the responses of all body builders will be within 21 mg of 173 mg.
e) 95% of the time, the difference between the average of the anabolic steroid use of the 20 body builders and the

true averageanabolicsteroiduseofallbodybuildersis21mg.
f) a slight chance, probability 5%, that either the average of all body builders is either more than 194 mg or less

than 152 mg.

4) For the following example, determine which interpretations are correct.

Patientswithchronickidneyfailuremaybetreatedbydialysistoremovetoxicwastesfromtheblood. Kidneyfailure and dialysis can cause other changes such as retention of phosphorus, which must be corrected by changes in diet. The phosphorus level for one patient was measured on six randomly selected occasions with ?̅ = 5.35. A 90% confidence interval estimate for the patient’s average blood phosphorus level was computed to be 4.8 to 5.9.

1. a) Weare90%confidentthattheaveragelevelofphosphorusinthepatient’sbloodissomewherebetween4.8and5.9.

2. b) We are 90% confident that the measurements of phosphorus level in the patient’s blood are between 4.8 and 5.9.

3. c) There is a 0.90 chance that the average phosphorus level in the patient’s blood is between 4.8 and 5.9.

4. d) Ninety percent of the time, we will obtain the interval 4.8 to 5.9 as an estimate to the averages phosphorus in the

   patient’s blood.

Answer 1

1) We are 95% sure that the average weekly dose of anabolic steroids used by body builders is between 152 mg and 194 mg.

Option C is correct.

2) The confidence interval procedure used in the above example gives intervals that contain the true mean 95% of the time.

Option A is correct.

3) 95% of the sample means from all possible samples of size 20 will differ from the true average weekly oral dose by no more than 21 mg.

Option C is correct.

4) Weare90%confidentthattheaveragelevelofphosphorusinthepatient’sbloodissomewherebetween4.8and5.9.

Option A is correct.