Question

A new type of fertilizer is being tested on a plot of land at Schrute Farms to see whether it increasesthe amount of beets produced. The mean number of pounds of beets produced on this plot with the oldfertilizer is 400 pounds. Dwight believes that the mean yield will increase with the new fertilizer. He definesthe following hypotheses, where μ = true mean beet yield of the plot with new fertilizer:H0: μ = 400 lb vs. H1: μ > 400 lb.(a) Describe a Type I error in this situation.(b) What might be a consequence of committing a Type I error?(c) Describe a Type II error in this situation.(d) What might be a consequence of committing a Type II error?

Answer 1

Explanation:

The null hypothesis is

H0: μ = 400 lb

The alternative hypothesis is

H1: μ > 400 lb

a) A type I error is said to occur when we make the mistake of rejecting the null hypothesis even when it is true. In this situation, a type I error would be made if we conclude that the mean yield will increase with the new fertilizer when the new fertilizer will not increase the yield.

b) the consequence of committing a type I error is that money would be wasted in buying new fertilizers and the yield would not improve.

c) A type II error is said to occur when we make the mistake of accepting the null hypothesis even when it is false. In this situation, a type II error would be made if we conclude that the mean yield will not increase with the new fertilizer when the new fertilizer will actually increase the yield.

d) the consequence of committing a type II error is that yield would remain low when we could have increased it by buying and applying new fertilizer.