Legend has it that the trees in a certain forest are, on average, 100 feet tall. A botanist wishes to check, so goes to the forest and measures the heights of 121 trees selected at random. The measured trees have a mean height of 97 feet, and a standard deviation of 22 feet.

a. What is the null hypothesis?

b. What is the alternative hypothesis?

c. What would constitute a Type I error?

d. What would constitute a Type II error?

e. Construct a 95% confidence interval for the mean heights of these trees.

f. What do you conclude about this legend, and why?