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 1.329 1.340 1.074 1.226 0.938 1.006 1.179 1.286
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.)

x =
s =

Describe the distribution of these differences using words.
The distribution is Normal.The distribution is uniform.     The distribution is right skewed.The distribution is left skewed.The sample is too small to make judgments about skewness or symmetry. [Correct: Your answer is correct.]
(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 =   [Incorrect: Your answer is incorrect.]

Give the degrees of freedom.
[Correct: Your answer is correct.]

Give the P-value. (Round your answer to four decimal places.)
[Correct: Your answer is correct.]

Give your conclusion.
We cannot reject H0 based on this sample.We can reject H0 based on this sample.      [Correct: Your answer is correct.]
(c) 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.)
  ,  

(d) 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. Comment 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.
The subjects from this sample, test results, and confidence interval are representative of future subjects.The subjects from this sample may be representative of future subjects, but the test re

Explanation / Answer

a)

x = -0.00175

s(dbar) = 0.0115

b)

SE = s(dbar)/sqrt(n) = 0.0041

Test Statisitcs, t = dbar/SE = -0.4319

degrees of freedom = n-1 = 7

p-value = 0.6788

c)

x1bar - x2bar = -0.00175

SE = 0.0041

CI = 95%

DF = 7

t-value = 2.3646

ME = t*SE = 0.0096

Confidence Interval = (x1bar - x2bar) +/- ME

Lower bound = -0.01133

Upper bound = 0.00783

Confidence Interval (-0.0113 , 0.0078 )

d)

If the subjects are not randomly selected, we will not get correct information about the population

Operator 1 Operator 2 dbar 1.329 1.323 0.006 1.34 1.322 0.018 1.074 1.073 0.001 1.226 1.233 -0.007 0.938 0.934 0.004 1.006 1.019 -0.013 1.179 1.184 -0.005 1.286 1.304 -0.018

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