A chemical company is developing a new fertilizer for tomatoes and wants to know if tomatoes grown with it are larger than the known mean weight of tomatoes grown with their current fertilizer, which is 1.2 pounds.
Researchers will feed 30 young plants with the new fertilizer and measure the mean weight of fruits produced
by the plants.
(a) Define the parameter and state the null and alternative hypotheses for this test.
(b) Describe a Type II error in the context of this study and give one possible consequence.
(c) Prior to performing the experiment, the company researchers determined that for a one-sided test of
significance using 30 plants, the power of this test at a 1% significance level to detect u= 1.4 is
only 0.30. Explain what the power of the test measures in the context of the problem.
(d) Based on your answers to (b) and (c), would a=0.10 or a= 0.01 be a better significance level for
this test? Explain your choice.