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 42 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 σ = 7.60 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 uniformσ is unknownthe distribution of weights is normaln is largeσ is known

(c) Interpret your results in the context of this problem.

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.    We are 1% confident that the true average blood plasma volume in male firefighters falls within this interval.We are 99% confident that the true average blood plasma volume in male firefighters falls within this interval.

(d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.40 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)
male firefighters

Answer 1

Ans:

a)

Margin of error=2.576*7.60/sqrt(42)=3.02

lower limit=37.50-3.02=34.48

upper limit=37.50+3.02=40.52

b)n is large,σ is known

c)We are 99% confident that the true average blood plasma volume in male firefighters falls within this interval.

d)

Sample size required,n=(2.576*7.60/2.4)^2=66.54