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 = 7.00 ml/kg for the distribution of blood plasma.

(a) Find a 95% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Use 2 decimal places.)

lower limit
upper limit
moe

(d) Find the sample size necessary for a 95% confidence level with maximal/marginal error of estimate E = 2.80 for the mean plasma volume in male firefighters.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 37.5

Population standard deviation = = 7

Sample size = n = 46

(a)

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * (7 / 46)

= 2.02

moe = 2.02

At 95% confidence interval estimate of the population mean is,

- E < < + E

37.5 - 2.02 < < 37.5 + 2.02

35.48 < < 39.52

(35.48 , 39.52)

Lower limit = 35.48

Upper limit = 39.52

moe = 2.02

(d)

E = 2.80

Sample size = n = ((Z_/2 * ) / E)²

= ((1.96 * 7) / 2.80)²

= 24

Sample size = 24