# Question

Let X equal the forced vital capacity (FVC) in liters for a female college student. (The FVC is the amount of air that a student can force out of her lungs.) Assume that the distribution of X is approximately N(μ, σ2). Suppose it is known that μ = 3.4 liters. A volleyball coach claims that the FVC of volleyball players is greater than 3.4. She plans to test her claim with a random sample of size n = 9.
(a) Define the null hypothesis.
(b) Define the alternative (coach’s) hypothesis.
(c) Define the test statistic.
(d) Define a critical region for which α = 0.05. Draw a figure illustrating your critical region.
(e) Calculate the value of the test statistic given that the random sample yielded the following FVCs: