Question

1. A new type of fertilizer is being tested on a plot of land at Schrute Farms to see whether it increases

the amount of beets produced. The mean number of pounds of beets produced on this plot with the old

fertilizer is 400 pounds. Dwight believes that the mean yield will increase with the new fertilizer. He defines

the 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

A new type of fertilizer is being tested on a plot of land at Schrute Farms to see whether it increases the amount of beets produced.

The mean number of pounds of beets produced on this plot with the oldf fertilizer is 400 pounds.

Dwight believes that the mean yield will increase with the new fertilizer.

We want to test that the mean yeild is greater than 400 pounds.

Ho:- u = 400 vs Ha: u > 400

1) Type I error

Reject Ho when it is true.

We reject Ho & conclude that mean yeild is greater than 400 pounds but actually mean yeild is 400 pounds.

Or

We reject Ho & conclude that mean yeild is increased but actually mean yeild is not increased.

2) consequences of tyeo I error

We will use the new type of fertilizer but actually it is not more effective in increased yeild.

3) type II error

Fail to reject Ho when it is false.

We may conclude that yeild is not increased but actually it is increased

Or

We may conclude that fertilizer doesn't increase yeild but actually it increases yeild

4) by making type II error

We are falsely fail to reject Ho

So may say that the fertilizer is not useful in increasing yeild but actually it is effective

& We do not use the new fertilizer.

So yeild cannot be increased