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 44 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 ó = 7.20 ml/kg for the distribution of blood plasma.

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 44 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 ó = 7.20 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_______

Answer 1

99% confidence interval = mean ± 2.575 SD

http://en.wikipedia.org/wiki/Margin_of_error

Answer 2

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 41 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 = 7.40 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________

Answer 3

To find the 99% confidence interval for the population mean blood plasma volume in male firefighters, you can use the formula:

Confidence Interval = x ± z * σ / √n

Where:
- x is the sample mean (37.5 ml/kg)
- z is the z-score corresponding to the desired confidence level (99% confidence level corresponds to a z-score of 2.576)
- σ is the standard deviation of the distribution of blood plasma (7.20 ml/kg)
- n is the sample size (44)

Let's plug in the values and calculate the confidence interval:

Confidence Interval = 37.5 ± 2.576 * 7.20 / √44

Calculating the values inside the formula:

Confidence Interval = 37.5 ± 2.576 * 7.20 / √44
= 37.5 ± 2.576 * 7.20 / 6.64

Calculating the numerator:

37.5 ± 2.576 * 7.20 = 37.5 ± 18.5472
= 18.9522 to 56.0478

Now, let's calculate the margin of error:

Margin of Error = (upper limit - lower limit) / 2

Plugging in the values:

Margin of Error = (56.0478 - 18.9522) / 2
= 37.10 / 2
= 18.55

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

Lower Limit: 18.95 ml/kg
Upper Limit: 56.05 ml/kg

And the margin of error is 18.55 ml/kg.