Dual-energy X-ray absorptiometry (DxA) is a technique for measuring bone health.

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 content (TBBMC). A highly skilled operator is required to take the measurements. Recently, a new DXA machine was purchased by a research lab and two operators 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 operato 1.328 1.339 1.078 1.226 0.938 1.004 1.182 1.289 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 operator 1 and the TBBMC for operator 2. (Operator 1 minus operator 2. Round your answers to four decimal places.) 1.1735 X Enter a number. Describe the distribution of these differences using words. The distribution is right skewed. O The distribution is uniform O The sample is too small to make judgments about skewness or symmetry. O The distribution is Normal O The distribution is left skewed (b) se a significance test to examine the nu hypothesis that the two operators have the same mean. Give the test statistic. Round your answer to three decimal places.) Give the degrees of freedom.

Explanation / Answer

a) x bar = -0.001

s = 0.0021

b) x1 = 1.173 , x2 = 1.174 , s1 = 0.151 , s2 = 0.149 , n1 = n2 = 8

SE = sqrt[(s12/n1) + (s22/n2)]
SE = sqrt[(0.1512/8) + (0.1492/8]

= 0.075

t = [ (x1 - x2) - d ] / SE

= [(1.173 - 1.174) - 0] / 0.075

= -0.013

df = 8 + 8 -2 = 14

p value

P value is calculated using t = -0.013 , df = 14

p value = .4949

we cannot reject H0 based on this sample

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