(EX) 6.39 DXA scanners. A dual-energy X-ray absorptiometry (DXA) scanner is used

Question

(EX) 6.39 DXA scanners.

A dual-energy X-ray absorptiometry (DXA) scanner is used to measure bone mineral density for people who may be at risk for osteoporosis. One company believes that its scanner is not giving accurate readings. To assess this, the company uses an object called a “phantom” that has known mineral density = 1.4 grams per square centimeter. The company scans the phantom 10 times and compares the sample mean reading  with the theoretical mean using a significance test. Choose the correct null and alternative hypotheses for this test:

H0:1.4g/cm2 Ha:=1.4g/cm2

H0:< 1.4g/cm2 Ha:=1.4g/cm2

H0:=1.4g/cm2 Ha:1.4g/cm2

H0:=1.4g/cm2 Ha:< 1.4g/cm2

(EX) 6.39 DXA scanners.

A dual-energy X-ray absorptiometry (DXA) scanner is used to measure bone mineral density for people who may be at risk for osteoporosis. One company believes that its scanner is not giving accurate readings. To assess this, the company uses an object called a “phantom” that has known mineral density = 1.4 grams per square centimeter. The company scans the phantom 10 times and compares the sample mean reading  with the theoretical mean using a significance test. Choose the correct null and alternative hypotheses for this test:

H0:1.4g/cm2 Ha:=1.4g/cm2

H0:< 1.4g/cm2 Ha:=1.4g/cm2

H0:=1.4g/cm2 Ha:1.4g/cm2

H0:=1.4g/cm2 Ha:< 1.4g/cm2

Explanation / Answer

Null Hypothesis: mean = 1.4
Alternative: mean does not equal 1.4

Note that the hypotheses must refer to parameters, not statistics. So "average =1.4" would be wrong.

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