Dual-energy X-ray absorptiometry (DXA) is a technique for measuring bone health. One of the most common measures is total body bone mineral con- tent (TBBMC). A highly skilled operator is required to take the measurements. Recently, a new DXA machine was purchased by a research lab and two oper- ators were trained to take the measurements. TBBMC for eight subjects was measured by both operators. The units are grams (g). A comparison of the means for the two operators provides a check on the training they received and allows us to determine if one of the operators is producing measurements that are consistently higher than the other. Here are the data: Subject 4 1.328 | 1.335 | 1.079 1.227 | 0.936 | 1.006 | 1.178 | 1.287 1.323 | 1.322 | 1.073 | 1.233 0.934 | 1.019 | 1.184 Operator 1 2 3 6 8 1 1.304

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Dual-energy X-ray absorptiometry (DXA) is a technique for measuring bone
health. One of the most common measures is total body bone mineral con-
tent (TBBMC). A highly skilled operator is required to take the measurements.
Recently, a new DXA machine was purchased by a research lab and two oper-
ators were trained to take the measurements. TBBMC for eight subjects was
measured by both operators. The units are grams (g). A comparison of the
means for the two operators provides a check on the training they received and
allows us to determine if one of the operators is producing measurements that
are consistently higher than the other. Here are the data:
Subject
4
Оperator
5
1.328 1.335 1.079 | 1.227 | 0.936 1.006| 1.178 | 1.287
1.323 1.322| 1.073 1.233 0.934 | 1.019 | 1.184 1.304
1
2
3
6
7
8
1
2
a) Are the two operator groups Independent or Dependent? Explain.
b) Do we need to assume that both groups are Normally distributed? Explain.
c) Use a significance test to examine the null hypothesis that the two op-
erators have the same mean. Make your conclusion based on your test
statistics and critical value where a = .02.
d) Use a 98% confidence interval to provide a range of differences that are
compatible with these data. What can you conclude? Is one of operators
significantly better than the other? Explain.
e) The eight subjects used for this comparison were not a random sample.
In fact, they were friends of the researchers whose ages and weights were
similar to the types of people who would be measured with this DXA. Com-
ment on the appropriateness of this procedure for selecting a sample, and
discuss any consequences regarding the interpretation of the significance
testing and confidence interval results.
Transcribed Image Text:Dual-energy X-ray absorptiometry (DXA) is a technique for measuring bone health. One of the most common measures is total body bone mineral con- tent (TBBMC). A highly skilled operator is required to take the measurements. Recently, a new DXA machine was purchased by a research lab and two oper- ators were trained to take the measurements. TBBMC for eight subjects was measured by both operators. The units are grams (g). A comparison of the means for the two operators provides a check on the training they received and allows us to determine if one of the operators is producing measurements that are consistently higher than the other. Here are the data: Subject 4 Оperator 5 1.328 1.335 1.079 | 1.227 | 0.936 1.006| 1.178 | 1.287 1.323 1.322| 1.073 1.233 0.934 | 1.019 | 1.184 1.304 1 2 3 6 7 8 1 2 a) Are the two operator groups Independent or Dependent? Explain. b) Do we need to assume that both groups are Normally distributed? Explain. c) Use a significance test to examine the null hypothesis that the two op- erators have the same mean. Make your conclusion based on your test statistics and critical value where a = .02. d) Use a 98% confidence interval to provide a range of differences that are compatible with these data. What can you conclude? Is one of operators significantly better than the other? Explain. e) The eight subjects used for this comparison were not a random sample. In fact, they were friends of the researchers whose ages and weights were similar to the types of people who would be measured with this DXA. Com- ment on the appropriateness of this procedure for selecting a sample, and discuss any consequences regarding the interpretation of the significance testing and confidence interval results.
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