Question

In Green Bay and Appleton, Wisconsin, the average height of hemlock trees is normally distributed within each city. Lilith is trying to determine if one town’s trees are taller than the other town’s trees before deciding where to start her tree farm. Her horticultural knowledge reveals that the standard deviation of the height of similar types of trees is the same everywhere in Wisconsin. So she conducts a test to compare the two populations assuming the same variance within each city. In Green Bay, Lilith sampled 100 trees and found that the average height of trees is 20 feet. In Appleton, she also sampled 100 and found that the average height is 21 feet. In the pooled sample, the estimated standard deviation is 2 feet. What is the absolute value of the t-statistic if the null hypothesis is that the two city’s trees are the same height?

Select one:

a. 0.5

b. 4.5

c. 2.5

d. 3.5

e. 1.5

Answer 1

The absolute value of t statistic will be:

$t = \frac{21-20}{2\sqrt{\frac{1}{100} + \frac{1}{100}}}$

t = 3.5

Option D is correct.