A certain type of cattail plant has a height that is normally distributed with a mean of 1.5 feet and a standard deviation of 0.1 feet. Suppose a biologist wishes to test if cattails growing in polluted waters are, on average, shorter. He takes measurements of 20 randomly selected cattails in a polluted lake and measures their lengths. He obtains a mean length of 1.45 feet.
a. If he were to conduct a hypothesis test for his theory, what would be the null and alternative hypotheses?
b. Compute the value of the test statistic.
c. Compute the p-value.
d. What conclusion would he reach based on the results of his hypothesis test? Use α = 0.05.