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:

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.)

(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 =  

Give the degrees of freedom.


Give the P-value. (Round your answer to four decimal places.)

(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.)

Subject Operator 1 2 3 4 5 6 7 8 1 1.326 1.342 1.078 1.228 0.937 1.008 1.181 1.289 2 1.323 1.322 1.073 1.233 0.934 1.019 1.184

1.304

Explanation / Answer

a)

1

2

Di

Di-D

(Di-D)^2

1.326

1.323

0.003

0.003375

1.13906E-05

1.342

1.322

0.02

0.020375

0.000415141

1.078

1.073

0.005

0.005375

2.88906E-05

1.228

1.233

-0.005

-0.00463

2.13906E-05

0.937

0.934

0.003

0.003375

1.13906E-05

1.008

1.019

-0.011

-0.01062

0.000112891

1.181

1.184

-0.003

-0.00262

6.89062E-06

1.289

1.304

-0.015

-0.01463

0.000213891

D

-0.00037

0

0.000821875

E(Di-D)^2

E(Di-D)

b)

D=ED/n=-0.00037

S.D=sqrt(E(Di-D)2/n-1)=0.0108

tSTAT=D- /S.D/sqrt(n)

Where tSTAT has n - 1 d.f

tSTAT=-0.00037-0/0.0108/sqrt(8)

      =-0.0968

For 7 DF and a value as 0.05 (0.025 on each side), +-2.3646 is the critical value. Hence, cannot reject H0. The P-Value is .926211.

c)

D+-t S.D/sqrt(n)

-0.00037-2.3646(0.0108/sqrt(8) to -0.00037+2.3646(0.0108/sqrt(8))

=-0.00037-0.009 to -0.00037+0.009

=-0.00863 to 0.00863

1

2

Di

Di-D

(Di-D)^2

1.326

1.323

0.003

0.003375

1.13906E-05

1.342

1.322

0.02

0.020375

0.000415141

1.078

1.073

0.005

0.005375

2.88906E-05

1.228

1.233

-0.005

-0.00463

2.13906E-05

0.937

0.934

0.003

0.003375

1.13906E-05

1.008

1.019

-0.011

-0.01062

0.000112891

1.181

1.184

-0.003

-0.00262

6.89062E-06

1.289

1.304

-0.015

-0.01463

0.000213891

D

-0.00037

0

0.000821875

E(Di-D)^2

E(Di-D)

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