Question

PLEASE HELP WILL GIVE EXTRA POINTS

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.
Part B: Using a significance level of α = 0.05, what can you conclude from the context of this study?

Answer 1

Part A

The p-value indicates that the largest probability of having the two remedies having a difference as observed or larger than as observed being equal to 0.3822

Part B:

Given that the p-value of 0.3822 is larger than the significance level α of 0.05, we fail to reject the null hypothesis and we conclude that there is enough statistical evidence to suggest that the salvage rates are the same for Remedy A and B

Explanation:

The p-value

The test statistic is given as follows;

`Z=\frac{\hat{p}_1-\hat{p}_2}{\sqrt{\hat{p}(1-\hat{p})\left ((1)/(n_(1))+(1)/(n_(2)) \right )}}`

`\hat p_1` = 35/220 = 7/44

`\hat p_2` = 39/230

`\hat p` = 74/220 = 37/110

We get our test statistic z = -0.2996381

Part A

The p-value indicates that the largest probability of having the two remedies having a difference as observed or larger than as observed being equal to 0.3822

Part B:

Given that the p-value of 0.3822 is larger than the significance level α of 0.05, we fail to reject the null hypothesis and we conclude that there is enough statistical evidence to suggest that the salvage rates are the same for Remedy A and B.