Total plasma volume is important in determining the required plasma component in
ID: 3151357 • Letter: T
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 47 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 = 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? (Use 2 decimal places.)
(b) What conditions are necessary for your calculations? (Select all that apply.)
is unknownthe distribution of weights is normalthe distribution of weights is uniform is knownn is large
(c) Give a brief interpretation of 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.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 0.01.1% of the intervals created using this method will contain the true average blood plasma volume in male firefighters.
(d) Find the sample size necessary for a 99% confidence level with maximal/marginal error of estimate E = 2.90 for the mean plasma volume in male firefighters.
Explanation / Answer
a)
z for 99% confidence interval = 2.58
Margin of error (MOE) = z*SD/sqrt(n) = (2.58*7.2)/sqrt(47) = 2.71
Lower limit = 37.5 - 2.71 = 34.79
Upper Limit = 37.5 + 2.71 = 40.21
b)
The distribution of weights is normal
is known
n is large
c)
The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99.
d)
Margin of error (MOE) = z*SD/sqrt(n)
=>2.9 = (2.58*7.2)/sqrt(n)
=>sqrt(n) = (2.58*7.2)/2.9
=> n = 41.03 or 41 Answer
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.