Total plasma volume is important in determining the required plasma component in blood replacement theory for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that sample of 61 male firefighters are tested and that they have a plasma volume sample mean of x = 39.5 ml/kg (milliliters of plasma per kilogram body weight). Assume that o = 7.50 ml/kg for the distribution of blood plasma. Find the margin of error for 98% confidence level of the population mean blood plasma volume in male firefighters. Round your answer to two decimal places.
Answer
a. 2.24 ml/kg
b. 0.94 ml/kg
c. 51.90 ml/kg
d. 0.34 ml/kg
e. 0.29 ml/kg
To find the margin of error for a 98% confidence level, you will need to use the formula:
Margin of Error = Critical Value * Standard Deviation / Square Root of Sample Size
The critical value can be found using a z-table or a calculator. For a 98% confidence level, the critical value is approximately 2.33.
Given information:
Sample Mean (x) = 39.5 ml/kg
Standard Deviation (o) = 7.50 ml/kg
Sample Size (n) = 61
Now, let's calculate the margin of error:
Margin of Error = 2.33 * 7.50 / sqrt(61)
Using a calculator, you can calculate the square root of 61, which is approximately 7.81.
Margin of Error = 2.33 * 7.50 / 7.81
The result is approximately 2.24 ml/kg.
Therefore, the margin of error for a 98% confidence level of the population mean blood plasma volume in male firefighters is 2.24 ml/kg.
So, the correct answer is (a) 2.24 ml/kg.