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* = 8.00
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 unknown

the distribution of weights is uniform

the distribution of weights is normal

*σ* is known

*n* is large

(c) Interpret your results in the context of this problem.

1% of the intervals created using this method will contain the true average blood plasma volume in male firefighters.

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 0.01.

The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99.

(d) Find the sample size necessary for a 99% confidence level with
maximal margin of error *E* = 2.00 for the mean plasma
volume in male firefighters. (Round up to the nearest whole
number.)

male firefighters

Answer #1

The statistical software output for this problem is:

Hence,

a) Lower limit = 34.59

Upper limit = 40.41

Margin of error = (40.41 - 34.59)/2 = 2.91

b) the distribution of weights is normal

*σ* is known

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

d) For 99% CI, z = 2.576

So,

Sample size required

n = **107** male firefighters

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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 42 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 = 7.90 ml/kg for the
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plasma component in blood replacement therapy for a person
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a plasma volume sample mean of x = 37.5 ml/kg (milliliters
plasma per kilogram body weight). Assume that σ = 8.00
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a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma
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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 42 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.
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plasma component in blood replacement therapy for a person
undergoing surgery. Plasma volume is influenced by the overall
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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
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undergoing surgery. Plasma volume is influenced by the overall
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random sample of 45 male firefighters are tested and that they have
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