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 | 1.329 | 1.338 | 1.075 | 1.229 | 0.937 | 1.006 | 1.179 | 1.287 |
|---|
| 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 usingwords.
___The distribution is uniform.
___The distribution is left skewed.
___The sample is too small to make judgments about skewness orsymmetry.
___The distribution is Normal.The distribution is rightskewed.
(b) Use a significance test to examine the nullhypothesis that the two operators have the same mean. Give the teststatistic. (Round your answer to three decimalplaces.)
t = ________
Give the degrees of freedom.__________
Give the P-value. (Round your answer to fourdecimal places.) ___________
Give your conclusion. (Use the significance level of5%.)
____We cannot reject H0based on this sample.
____We can reject H0 basedon this sample.
(c) The sample here is rather small, so we may not have muchpower to detect differences of interest. Use a 95% confidenceinterval to provide a range of differences that are compatible withthese data. (Round your answers to four decimal places.)
(______________ , _____________ )
,
(d) The eight subjects used for this comparison were nota random sample. In fact, they were friends of the researcherswhose ages and weights were similar to the types of people whowould be measured with this DXA machine. Comment on theappropriateness of this procedure for selecting a sample, anddiscuss any consequences regarding the interpretation of thesignificance-testing and confidence interval results.
____The subjects from this sample may be representative offuture subjects, but the test results and confidence interval aresuspect because this is not a random sample.
_____The subjects from this sample, test results, and confidenceinterval are representative of future subjects.
