Question

Total plasma volume is important I. determining the required plasma compound. 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 space of 47 male firefighters are tested and that they have a plasma volume example mean of 37. 5 ml/kg ( millimeters plasma per kilogram body weight)

Assume that the standard deviation = 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 answer to two decimal places. )

lower limit____

upper limit ______

margin of error _____

b) What conditions are necessary for your calculations? ( Select all that apply. )

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

d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 3.00 for the plasma volume in male firefighters. ( Round up to the nearest whole number. )_______ male firefighters

Answer 1

a)

z value at 99% = 2.576

CI = mean +/- z *(s/sqrt(n))
= 37.5 +/- 2.576 *(7.20/sqrt(47))
= (34.79 , 40.21)

Lower limit = 34.79
upper limit = 40.21

Margin of error = 2.5 76 *(7.20/sqrt(47))
= 2.71

b)

The sample must be reasonably random.
The data must be from a normal distribution or large sample (need to check n ≥ 30 ).
σ must be known.
The sample must be less than 10% of the population so that sigma/sqrt(n) is valid for the standard
deviation of the sampling distribution of x . bar

c)

We are 99% confident taht the population mean blood plasma volume in male firefighters is between 34.79 and 40.21

d)

ME = 3

z value at 99% = 2.576

ME= z *(s/sqrt(n))
3 = 2.576 *(7.20/sqrt(n))
n = (2.576 *7.20/3)

n = 6