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 46 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 = 7.80 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

n is large

the distribution of weights is uniform

the distribution of weights is normal

C:Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.60 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)

male firefighters

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 37.5

Population standard deviation =    = 7.80

Sample size = n = 46

a) At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005 = 2.576

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

E = 2.576 * (7.80 /  46 )

E = 2.96

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

  ± E

37.5 ± 2.96   

( 34.54, 40.46 )  

lower limit = 34.54

upper limit = 40.46

margin of error = 2.96

b) σ is known

n is large  

c) margin of error = E = 2.60

sample size = n = [Z/2* / E] 2

n = [2.576 * 7.80 / 2.60]2

n = 59.72

Sample size = n = 60 male firefighters