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 = 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

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

Interpret your results in the context of this problem.

Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.40 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)

male firefighters

Weatherwise magazine is published in association with the American Meteorological Society. Volume 46, Number 6 has a rating system to classify Nor'easter storms that frequently hit New England states and can cause much damage near the ocean coast. A severe storm has an average peak wave height of 16.4 feet for waves hitting the shore. Suppose that a Nor'easter is in progress at the severe storm class rating. (a) Let us say that we want to set up a statistical test to see if the wave action (i.e., height) is dying down or getting worse. What would be the null hypothesis regarding average wave height?

If you wanted to test the hypothesis that the storm is getting worse, what would you use for the alternate hypothesis?

If you wanted to test the hypothesis that the waves are dying down, what would you use for the alternate hypothesis?

Suppose you do not know if the storm is getting worse or dying out. You just want to test the hypothesis that the average wave height is different (either higher or lower) from the severe storm class rating. What would you use for the alternate hypothesis?

For each of the tests in parts (b), (c), and (d), would the area corresponding to the P-value be on the left, on the right, or on both sides of the mean?