Question

Total plasma volume is important in determining the reauired 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. Assume that SD = 7.80 ml/kg for the distribution of blood plasma.

(a) Find a 99% confidence interval for the population mean blood plasma volhme in make fire fighters.

lower limit- 34.37

upper limit- 40.63

margin of error- 3.15

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

- SD is unknown

- n is large

- the distribution of weights is uniform

- SD is known

- the distribution of weights is normal

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

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 37.5

Population standard deviation =    = 7.80

Sample size = n = 41

a) At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z_0.005 = 2.576

Margin of error = E = Z/2 * ( /n)

E = 2.576 * (7.80 /  41 )

E = 3.14

At 99% confidence interval estimate of the population mean is,

  ± E

37.5 ± 3.14

( 34.36, 40.64)  

lower limit = 34.36

upper limit = 40.64

margin of error = 3.14

b) n is large

SD is known

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

d) margin of error = E = 3.00

sample size = n = [Z_/2* / E] ²

n = [2.576 * 7.80 / 3.00]²

n = 44.85

Sample size = n = 45 male firefighters.