Dual-energy X-ray absorptiometry (DXA) is a technique formeasuring bone health. One of the most common measures is totalbody bone mineral content (TBBMC). A highly skilled operator isrequired to take the measurements. Recently, a new DXA machine waspurchased by a research lab and two operators were trained to takethe measurements. TBBMC for eight subjects was measured by bothoperators. The units are grams (g). A comparison of the means forthe two operators provides a check on the training they receivedand allows us to determine if one of the operators is producingmeasurements that are consistently higher than the other. Here arethe data:

	Subject
Operator	1	2	3	4	5	6	7	8
1	1.327	1.336	1.078	1.227	0.938	1.004	1.180	1.288
2	1.323	1.322	1.073	1.233	0.934	1.019	1.184	1.304

(a) Take the difference between the TBBMC recorded for Operator1 and the TBBMC for Operator 2. (Use Operator 1 minus Operator 2.Round your answers to four decimal places.)

x	=
s	=

Describe the distribution of these differences using words.

(b) Use a significance test to examine the null hypothesis that thetwo operators have the same mean. Give the test statistic. (Roundyour answer to three decimal places.)
t =  

Give the degrees of freedom.


Give the P-value. (Round your answer to four decimalplaces.)


Give your conclusion.

We can reject H₀ based on this sample or Wecannot reject H₀ based on thissample.    

(c) The sample here is rather small, so we may not have much powerto detect differences of interest. Use a 95% confidence interval toprovide a range of differences that are compatible with these data.(Round your answers to four decimal places.

(d) The eight subjects used for this comparison were not a randomsample. In fact, they were friends of the researchers whose agesand weights were similar to the types of people who would bemeasured with this DXA. Comment on the appropriateness of thisprocedure for selecting a sample, and discuss any consequencesregarding the interpretation of the significance testing andconfidence interval results.

The subjects from this sample, test results, and confidenceinterval are representative of future subjects. OR

The subjects from this sample may be representative of futuresubjects, but the test results and confidence interval are suspectbecause this is not a random sample