Question

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 = 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    ____

(b) What conditions are necessary for your calculations? (Select all that apply.)

__ σ is unknown

__ the distribution of weights is uniform

__ n is large

__ σ is known

__ the distribution of weights is normal

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

The probability that this interval contains the true blood plasma volume in male firefighters is 0.01.

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

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

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 = 2.70 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.) 

__  male firefighters

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