Total plasma volume is important in determining the required plasma component in

Question

Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 43 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that = 7.70 ml/kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit     upper limit     margin of error     (b) What conditions are necessary for your calculations? (Select all that apply.) the distribution of weights is normal n is large is unknown is known the distribution of weights is uniform (c) Interpret your results in the context of this problem. 1% of the intervals created using this method will contain the true average blood plasma volume in male firefighters. 99% of the intervals created using this method will contain the true average blood plasma volume in male firefighters.     The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01. The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99. (d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 3.00 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.) male firefighters

Explanation / Answer

a) here std error =std deviaiton/(n)1/2 =7.7/(43)1/2 =1.1742

for 99% CI; z=2.5758

therefore 99% confidence interval =sample mean -/+ Z*std error =34.4754 ; 40.5246

margin of error =z*std error =3.0246

b) distribution of weights is normal

is known

c)99% of the intervals created using this method will contain the true average blood plasma volume in male firefighters.

d)

here sample size required =(z*std deviation/E)2  =~44

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