Question

I have done some of this on my own but just cant seem to be able to finish this correctly.

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	1.327	1.335	1.077	1.226	0.936	1.004	1.181	1.288
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= -0.0022 (this is correct!)

s= 0.0100 (this is correct!)

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 = ??? (cant get right answer)

Give the degrees of freedom.

7 (this is correct!)

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

??? (cant get right answer)

Give your conclusion. (Use the significance level of 5%.)

a) We can reject H₀ based on this sample

or

b) We cannot 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.)

( , ) ??? (cant get right answer)

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 machine. 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.

a) The subjects from this sample may be representative of future subjects, but the test results and confidence interval are suspect because this is not a random sample.

or

b) The subjects from this sample, test results, and confidence interval are representative of future subjects.   

Answer 1

(a)

Following table shows the calculations:

Operator 1	Operator 2	d=operator1-operator 2	(d-mean)^2
1.327	1.323	0.004	3.91E-05
1.335	1.322	0.013	2.33E-04
1.077	1.073	0.004	3.91E-05
1.226	1.233	-0.007	2.26E-05
0.936	0.934	0.002	1.81E-05
1.004	1.019	-0.015	1.63E-04
1.181	1.184	-0.003	5.62E-07
1.288	1.304	-0.016	1.89E-04
Total		-0.018	7.03E-04

Sample size: n=8

Now,

The sample is too small to make judgments about skewness or symmetry.

(b)

Hypotheses are:

The test statistics will be

Degree of freedom: df=n-1=7

The P-value of the test is: 0.5450

We cannot reject H0 based on this sample.

(c)

For 95% confidence interval t critical value for df=7 is 2.4314. So required confidence interval will be

So required confidence interval is (-0.0109, 0.0064).

a) The subjects from this sample may be representative of future subjects, but the test results and confidence interval are suspect because this is not a random sample.