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 (9). 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 1.328 1.340 1.076 1.228 0.936 008 181 1.289 3610081 1.323 1.322 1.073 1.233 0.9341019 1.1841304 (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.) X = -0.0008 s = 0.0103 Describe the distribution of these differences using words. The distribution is Normal. The distribution is left skewed. o The sample is too small to make judgments about skewness or symmetry. o The distribution is right skewed. The distribution is uniform. (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= -0.220 Give the degrees of freedom. Give the P-value. (Round your answer to four decimal places.) 0.3747 X

Explanation / Answer

The statistical software output for this problem is:

Paired T hypothesis test:
D = 1 - 2 : Mean of the difference between Operator 1 and Operator 2
H0 : D = 0
HA : D 0
Hypothesis test results:

Hence,

t = -0.207

P - value = 0.8422

Difference Mean Std. Err. DF T-Stat P-value Operator 1 - Operator 2 -0.00075 0.0036290003 7 -0.20666849 0.8422

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