Question

In 2006, a study was conducted to compare two methods for assisting people experiencing trouble breathing as a result of an airway blockage. In Pittsburg, 350 patients were assigned randomly to one of two treatments: 150 to treatment 1 and 200 to treatment 2. A total of 250 patients survived the obstruction: 95 in the group receiving treatment 1 and 155 in the group receiving treatment 2. A test of significance was conducted on these hypotheses:

H₀: The survival rates for the two treatments are equal.
H_a: Treatment 2 produces a higher survival rate.

The statistical test resulted in a p-value of 0.0018.

Part A: What does the p-value measure in the context of this study? (3 points)

Part B: Based on this p-value and the study design, what conclusion can be drawn in the context of this study? Use a significance level of α = 0.05. (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) (10 points)

Answer 1

A. If there is no difference between the two treatments, the there is about a 0.18% chance of seeing the observed difference or larger by natural sampling variation.
B. Since, p-value < 0.05, so we can reject H0. Hence, the conclusion is that treatement 2 produces a higher survival rate.
C. Type I error is made when we reject H0 while it is actually true. Hence, we could have made type I error.
Possible consequence of this error is that we concluded that the treatment 2 produces a higher survival rate, when actually both the treatment produce the same survival rate.

Thank you for this question. Glad to help you. Please give a thumbs up ☺️