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

Operator 1 2 3 4 5 6 7 8

1 1.327 1.340 1.077 1.227 0.938 1.007 1.178 1.288

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 Operator 1 and the TBBMC for Operator 2. (Use Operator 1 minus Operator 2. Round your answers to four decimal places.)

s =

B. Use a significance test to examine the null hypothesis that the two operators have the same mean. Give the test statistic. (Round your answer to three decimal places.)
t =

C.Give the degrees of freedom=

D. The sample here is rather small, so we may not have much power to detect differences of interest. Use a 95% confidence interval to provide a range of differences that are compatible with these data. (Round your answers to four decimal places.)

x =

Explanation / Answer

B) test stat =d/std error =-0.3244

C) degree of freedom =n-1 =7

d) for 7 degree of freedom and 95% CI; t=2.3646

hence confidence interval =mean +/- t*std error = -0.0104 ; 0.0079

1 2 difference(d) 1.327 1.323 0.004 1.34 1.322 0.018 1.077 1.073 0.004 1.227 1.233 -0.006 0.938 0.934 0.004 1.007 1.019 -0.012 1.178 1.184 -0.006 1.288 1.304 -0.016 mean (x) -0.00125 std deviaition (s) 0.0109 std error= std dev/(n)^(1/2) 0.0039

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