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 5 |Operator 1 3 4 7 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 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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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.