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 41 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.)

σ is known

σ is unknown

the distribution of weights is normal

the distribution of weights is uniform

n is large

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

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 = 2.90 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)

Answer 1

We are given ,

sample mean ( ) = 37.5

Population standard deviation ( ) = 7.60

sample size (n) = 41

Confidence level = 0.99

Therefore  α = 1 - confidence level = 1 - 0.99 = 0.01

α/2 = 0.01/2 = 0.005 and 1 -  α/2 = 0.995

Therefore z score corresponding to area 0.995 on z score table is 2.58

So z = 2.58

Margin of error (E) = = = 3.06

Lower limit = - E = 37.5 - 3.06

Lower limit = 34.44

Upper limit = - E = 37.5 + 3.06

Upper limit = 40.56

b) Conditions necessary for the calculations are

is known

The distribution of weights is normal

n is large.

c) Interpretation :

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

d) Sample size n = = = 45.72

sample size = 46