Question

A study is performed involving two methods for removing harmful bacteria in 350 lakes in Florida. The lakes were treated randomly using one of two methods. Specifically, 150 were treated using Method A and 200 were treated using Method B. A total of 250 of the 350 lakes were bacteria-free after treatment, 95 from the Method A group, and 155 from the Method B group.

A significance test was performed for the following hypotheses and resulted in a p-value of 0.0018:

H0: Bacteria removal rates are the same for Method A and B
Ha: Method B has a higher bacteria removal 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?

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?

Answer 1

When the p-value is less than the level of significance then we say the test is significant i.e., we reject null hypothesis. Otherwise if the value if greater than the level of significance we accept null hypothesis.

A significance level of 0.05 is used to interpret the p-value. Since this is a two tailed test the alpha here is we will consider is (0.05/2=)0.0025. Test was performed for the following hypotheses and resulted in a p-value of 0.0018.

Since, 0.0018 < 0.0025. Thus we reject null hypothesis as the p value is less the level of significance.

Thus we conclude that  Method B has a higher bacteria removal rate. (Accept alternate hypothesis)

Based on your conclusion in part B, type of error—Type I could have been made.

One potential consequence of this error is that there will less Bacteria free lakes in Florida as we might take Method A to be equal in level with Method B and continue using Method A. Thus there is more risk of contaminated lakes (with virus).