A study is performed involving two remedies for midwest farm crops who experienced the worst drought in years. In the midwest, 450 crop fields were given randomly one of two remedies. Specifically, 220 were given Remedy A and 230 were given Remedy B. A total of 74 of the 450 crop fields were salvageable, 35 from Remedy A group and 39 from Remedy B group. A significance test was performed for the following hypotheses and resulted in a p-value of 0.3822: H0: Salvage rates are the same for Remedy A and B Ha: Remedy B has a greater salvage rate Part A: Interpret the p-value in terms of the context. (3 points) Part B: Using a significance level of α = 0.05, what can you conclude from the context of this study? (4 points) Part C: Based on your conclusion in part B, which type of error—Type I or Type II—could have been made? What is one potential consequence of this error? (3 points)

The p-value is well defined as per the probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was the truly observed value of the test statistic.

The p-value of the test was, p = 0.3822.

That is the probability that Remedy B has a greater salvage rate than A is 0.3822, given that rates are the same for Remedy A and B.

(B)

The significance level of the test is: α = 0.05.

A small p-value (typically ≤ 0.05) specifies strong evidence against the null hypothesis (H₀), so you discard H₀. A large p-value (> 0.05) specifies fragile proof against the H₀, so you fail to discard H₀.

The p-value of the test is very large. The null hypothesis will not be rejected.

Concluding that salvage rates are the same for Remedy A and B.

(C)

A type II error is a statistical word used within the circumstance of hypothesis testing that defines the error that take place when one is unsuccessful to discard a null hypothesis that is truly false.

In this case a type II error could have been made as the null hypothesis was not rejected.

The type II error could have been made because of the following reasons:

The sample size selected is too small.
Significance level of the test must be small.

As the sample selected is quite large, the only potential consequence of this error is that the significance level of the test must be small.