Question

In 2005, a study was conducted to compare two treatments for people who experienced a stroke. In Salt Lake City, 450 patients were assigned randomly to one of the two treatments: 220 to treatment 1 and 230 to treatment 2. A total of 74 patients survived the stroke: 35 in the group receiving treatment 1 and 39 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 0.3822.

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 the 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

Part A: The p-value measures the probability of getting the result when the given result is not really true. Therefore there is a 0.3822 probability that the test comes out to be significant when it is really not true. The lower the p-value, greater the test significance and we can reject the null hypothesis.

Part B: As the p-value here is 0.3822 > 0.05 which is the level of significance, therefore the test is not significant and we cannot reject the null hypothesis here, therefore we dont have sufficient evidence to reject the statement that the survival rates for the two treatments are equal.

Part C: Based on the part B, there is a probability of making a type II error which is the probability of retaining the false null hypothesis ( as we did not reject the null hypothesis here. )