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
Opertor	1	2	3	4	5	6	7	8
1	1.324	1.339	1.079	1.227	0.938	1.005	1.180	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. (Use Operator 1 minus Operator 2. Round your answers to four decimal places.)

            x=_______

         s=_______

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.

         Answer:______

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

         Answer:______

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.)

         Answer: (_____,_____)

Answer 1

Based on the given data,

Let D = Difference between measurement of the two operators (Operator 1 - Operator 2)

Since the measurements recorded by the both operators are on the same patients, this would be a case of paired sample test.

To test,

Vs

Where is the mean of the differences between the observations measured by the two operators.

The test statistic is given by,

where,   = Standard Deviation of D / , N = No. of paired samples

Substituting the required values,

Using excel,

Here, since the , we may accept the null hypothesis; there is not sufficient evidence to support the claim that one of the operators is producing measurements that are consistently higher than the other.

The 95% confidence interval for the difference is given by,

To obtain t from t tables, for 7 df, at alpha = 0.05, for one tailed test,

Substituting the required values,

95% Confidence Interval for D=