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 50 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 = 7.60 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 the distribution of weights is uniform σ is unknown the distribution of weights is normal n is large (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. 99% of the intervals created using this method will contain the true average blood plasma volume in male firefighters. 1% of the intervals created using this method will contain the true average blood plasma volume in male firefighters. The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01. (d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 3.00 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.) male firefighters

Answer 1

Solution:

Given:

Sample size = n= 50
Sample mean =
Population Standard Deviation =
Part a) Find 99% confidence interval for the population mean blood plasma volume in male firefighters.

Formula:

where

Z_c is z critical value for c = 0.99 confidence level.

Find Area = ( 1+c)/2 = ( 1 + 0.99 ) / 2 = 1.99 /2 = 0.9950

Thus look in z table for Area = 0.9950 or its closest area and find corresponding z critical value.

From above table we can see area 0.9950 is in between 0.9949 and 0.9951 and both are at same distance from 0.9950, Hence corresponding z values are 2.57 and 2.58

Thus average of both z values is 2.575

Thus Z_c = 2.575

Thus

Margin of Error =

Thus

Thus

Lower Limit = 34.43

Upper Limit = 40.27

Part b) What conditions are necessary for your calculations?

σ is known

n is large

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

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

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