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 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 = 7.50 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.)

n is large

the distribution of weights is norma

lσ is known

σ is unknown

the distribution of weights is uniform

(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.

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.

99% 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 margin of error E = 2.70 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)

Answer 1

(A) use Ti 84

STAT --> TESTS --> Zinterval

σ = 7.50

x = 37.5

n = 50

C-level = 0.99

Enter, then we get

lower limit = 34.45

Upper limit = 40.56

Margin of error = (upper limit - lower limit)/2 = (40.56-34.45)/2 = 3.06

(B) To use the z confidence interval, we need only known sigma value with a normal distribution of weights

So, option B and C (the distribution of weights is normal and σ is known)

(C) 1% or 0.01 proportion statements are incorrect as we have calculated 99% confidence interval., but not 1% confidence interval.

So, correct statement is "99% of the intervals created using this method will contain the true average blood plasma volume in male firefighters."

option D

(D) margin of error E = 2.70

z critical = 2.576 [From z table for 0.99 level]

σ = 7.50

sample size n = ((z*σ)/E)^2

=((2.576*7.5)/2.7)^2

= 7.156^2

= 51.202

= 51 (rounded to nearest whole number)