Dual-energy X-ray absorptiometry (DXA) is a technique formeasuring bone health. One of the most common measures is totalbody bone mineral content (TBBMC). A highly skilled operator isrequired to take the measurements. Recently, a new DXA machine waspurchased by a research lab, and two operators were trained to takethe measurements. TBBMC for eight subjects was measured by bothoperators. The units are grams (g). A comparison of the means forthe two operators provides a check on the training they receivedand allows us to determine if one of the operators is producingmeasurements that are consistently higher than the other. Here arethe data.

Subject Operator

1 2 3 4 5 6 7 8 1 1.326 1.338 1.077 1.228 0.938 1.008 1.1821.288

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 Operator1 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 right skewed.

The distribution is uniform.

The distribution is Normal.

The distribution is left skewed.

The sample is too small to make judgments about skewness orsymmetry.

(b) Use a significance test to examine the null hypothesis thatthe 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 decimalplaces.)

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

We can reject H0 based on this sample.

We cannot reject H0 based on this sample.

(c) The sample here is rather small, so we may not have muchpower to detect differences of interest. Use a 95% confidenceinterval to provide a range of differences that are compatible withthese data. (Round your answers to four decimal places.) ,

(d) The eight subjects used for this comparison were not arandom sample. In fact, they were friends of the researchers whoseages and weights were similar to the types of people who would bemeasured with this DXA machine. Comment on the appropriateness ofthis procedure for selecting a sample, and discuss any consequencesregarding the interpretation of the significance-testing andconfidence interval results.

The subjects from this sample, test results, and confidenceinterval are representative of future subjects.

The subjects from this sample may be representative of futuresubjects, but the test results and confidence interval are suspectbecause this is not a random sample.