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 50 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 = 7.20 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 normaln is largethe distribution of weights is uniformσ is unknownσ 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.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.

(d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.70 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)
male firefighters

Answer 1

given that

sample mean =m=37.5

sample size=n=50

SD=7.2

a)

now for 99% confidence level margin of error is given by

now

Lower limit of interval =m-E=37.5-2.63=34.87

Upper limit of interval =m+E=37.5+2.63 =40.13

Margin of error =E=2.63

b)

Necessary conditions are:

the distribution of weights is normal

sample are taken randomly

n is large

c)

since 99% confidence interval is defined as if there are many such intervals then 99% of them will contain true population mean hence

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

d)

Here E=2.70

Now

now for 99% confidence level margin of error is given by

Hence n~48