Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person

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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 40 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 = 7.20 ml/kg for the
distribution of blood plasma.
When finding an 99% confidence interval, what is the critical
value for confidence level? (Give your answer to two decimal
places.)
zc =
(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 limitupper limitmargin of error
(b)
What conditions are necessary for your calculations? (Select all
that apply.)
𝜎 is unknownthe distribution of volumes is
normaln is largethe distribution of volumes is
uniform𝜎 is known
(c)
Interpret your results in the context of this problem.
We are 1% confident that the true average blood plasma volume in
male firefighters falls within this interval.The probability that
this interval contains the true average blood plasma volume in male
firefighters is 0.99. We are 99% confident
that the true average blood plasma volume in male firefighters
falls within this interval.The probability that this interval
contains the true average blood plasma volume in male firefighters
is 0.01.
(d)
Which equation is used to find the sample
size n for
estimating 𝜇 when 𝜎 is known?
n =
n =
n =
n =
Find the sample size necessary for a 99% confidence level with
maximal margin of error E = 2.90 for
the mean plasma volume in male firefighters. (Round up to the
nearest whole number.)
male firefighters