For many important processes that occur in the body, direct measurement of characteristics of the process is not possible. In many cases, however, we can measure a biomarker, a biochemical substance that is relatively easy to measure and is associated with the process of interest. Bone turnover is the net effect of two processes: the breaking down of old bone, called resorption, and the building of new bone, called formation. A biomarker for bone formation measured was osteocalcin (OC), measured in the blood. The units are nanograms per milliliter (ng/ml). For the 31 subjects in the study the mean was 33.4 ng/ml. Assume that the standard deviation is known to be 19.6 ng/ml.

Required:
Give the margin of error and find a 95% confidence interval for the mean TRAP amount in young women represented by this sample.

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okpalawalter8 okpalawalter8 · Answer 1 · 2020-11-12T01:33:50+01:00

Answer:

The margin of error is [tex]E = 6.9 [/tex]

The 95% confidence interval is [tex] 26.5 < \mu < 40.3 [/tex]

Step-by-step explanation:

From the question we are told that

The sample size is n = 31

The mean is [tex]\mu = 33.4 \ ng/ml[/tex]

The standard deviation is [tex]\sigma = 19.6 \ ng/ml[/tex]

From the question we are told the confidence level is 95% , hence the level of significance is

[tex]\alpha = (100 - 95 ) \%[/tex]

=> [tex]\alpha = 0.05[/tex]

Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is

[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

=> [tex]E = 1.96 * \frac{19.6 }{\sqrt{31 } }[/tex]

=> [tex]E = 6.9 [/tex]

Generally 95% confidence interval is mathematically represented as

[tex]\= x -E < \mu < \=x +E[/tex]

=> [tex] 33.4 - 6.9 < \mu < 33.4 + 6.9 [/tex]

=> [tex] 26.5 < \mu < 40.3 [/tex]