Question

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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 47 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 o = 7.40 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.) On is large the distribution of weights is normal O ois unknown the distribution of weights is uniform O o is known (c) Give a brief interpretation of your results in the context of this problem. We are 99% confident that the true average blood plasma volume in male firefighters falls within this interval. The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99. We are 1% confident that the true average blood plasma volume in male firefighters falls within this interval. O The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01. (d) Find the sample size necessary for a 99% confidence level with maximal error of estimate E = 2.40 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.) male firefighters

Answer 1

solution:-

given that x̅ = 37.5 , σ = 7.40 , n = 47

(a) the z-critical value for 99% confidence from z table is 2.576

confidence interval

=> x̅ +/- z * σ/sqrt(n)

=> 37.5 +/- 2.576 * 7.40/sqrt(47)

=> 37.5 +/- 2.78

=> (34.72 , 40.28)

lower limit = 34.72

upper limit = 40.28

margin of error = 2.78

(b)what conditions are necessary for your calculations

=> n is large

=> σ is known

(c) interpret your results in the context of this problem

=> we are 99% confident that the true average blood plasma volume in male firefighters falls within this interval

(d) here given that E = 2.40

sample size formula

=> n = (z*σ/E)^2

=> n = (2.576*7.40/2.40)^2

=> n = 64