Question

In 2007, a study was conducted to compare two treatments for people experiencing a heart attack. In Atlanta, 300 patients were assigned randomly to treatments: 125 to treatment 1 and 175 to treatment 2. A total of 88 patients survived their heart attack: 32 in the group receiving treatment 1 and 56 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. Ha: Treatment 2 produces a higher survival rate. This statistical test resulted in a p-value of 0.1150.

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

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.

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

A)

P-value-

The p-value is the probability of type I error such that it is the probability of rejecting the null hypothesis when the null hypothesis is actually TRUE.

In this context, the p-value is 0.1150 which means there is an 11.50% chance that the result shows the survival rate for the treatment 2 higher but actually there was no difference in the survival rate for the two treatments

B)

P-value = 0.1150 > Significance level = 0.05

Since the p-value is greater than 0.05 at a 5% significance level, the null hypothesis is not rejected. Hence we can conclude that there is no difference in the survival rate for the two treatments.

C)

Since we failed to reject the null hypothesis, a type II error could have been made.

A Type II error is the probability of failing to reject the null hypothesis when the null hypothesis is actually FALSE.

Since we ended up concluding that there is no difference in the survival rate for the two treatments, there is a possibility which leads to false assumption and conclusion that treatment 2 has no significant effect on survival rates