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 1.326 1.337 1.079 1.229 0.936 1.009 1.179 1.289
2 1.323 1.322 1.073 1.233 0.934 1.019 1.184 1.304
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.)
X-bar=
S=
Describe the distribution of these differences using words. (which one is correct)
A- The distribution is left skewed.
B- The sample is too small to make judgments about skewness or symmetry.
C- The distribution is uniform.
D- The distribution is uniform.
E- The distribution is Normal.
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.)
Give the degrees of freedom and Give the P-value. (Round your answer to four decimal places.)
Can we reject H0 based on this sample, or can we reject H0 based on this sample?
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.)