Dual-energy X-ray absorptiometry (DXA) is a technique for measuring bonehealth. 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 wasmeasured by both operators. The units are grams (g). A comparison of themeans for the two operators provides a check on the training they received andallows us to determine if one of the operators is producing measurements thatare consistently higher than the other. Here are the data:Subject4Оperator51.328 1.335 1.079 | 1.227 | 0.936 1.006| 1.178 | 1.2871.323 1.322| 1.073 1.233 0.934 | 1.019 | 1.184 1.30412367812a) 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 teststatistics and critical value where a = .02.d) Use a 98% confidence interval to provide a range of differences that arecompatible with these data. What can you conclude? Is one of operatorssignificantly 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 weresimilar to the types of people who would be measured with this DXA. Com-ment on the appropriateness of this procedure for selecting a sample, anddiscuss any consequences regarding the interpretation of the significancetesting and confidence interval results.

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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 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

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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Concept explainers

2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.

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Question

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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