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 45male 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 = 7.30 ml/kgfor 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.)

the distribution of weights is normalnis largeσis unknownthe distribution of weights is uniformσis known

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

The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99.The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01.     We are 99% confident that the true average blood plasma volume in male firefighters falls within this interval.We are 1% confident that the true average blood plasma volume in male firefighters falls within this interval.

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

Answer 1

a) n = 45

Sample mean =

Population standard deviation =

Here Population standard deviation is known so we use z interval.

Confidence level = c = 0.99

99% confidence interval for the population mean blood plasma volume in male firefighters is

where e is margin of error

where zc is z critical value for (1+c)/2 = (1+0.99)/2 = 0.995

zc = 2.58 (From statistical table of z values)

e = 2.58 * 1.088

e = 2.81 (Round to 2 decimal)

Margin of error = 2.81

99% confidence interval for the population mean blood plasma volume in male firefighters is

99% confidence interval for the population mean blood plasma volume in male firefighters is (34.69, 40.31)

b)

Conditions:

the distribution of weights is normal, is known

c)

99% confidence interval for the population mean blood plasma volume in male firefighters is (34.69, 40.31)

Interprtation of confidence interval:

We are 99% confident that the true average blood plasma volume in male firefighters falls within this interval.

d)

Margin of error = e = 2.60

Population standard deviation =

Confidence level = c = 0.99

Sample size (n) :

where zc is z critical value for (1+c)/2 = (1+0.99)/2 = 0.995

zc = 2.58 (From statistical table of z values)

n = 52.47331

n = 52 (Round to nearest whole number)

Sample size = 52