A researcher is interested in determining whether acupuncture affects pain tolerance. An experiment is performed in which 15 students are randomly chosen from a large pool of university undergraduate volunteers. Each subject serves in two conditions. In both conditions, each subject receives a short-duration electric shock to the pulp of a tooth. The shock intensity is set to produce a moderate level of pain to the anaesthetized subject. After the shock is terminated, each subject rates the perceived level of pain on a scale of 0–10, with 10 being the highest level. In the experimental condition, each subject receives the appropriate acupuncture treatment prior to receiving the shock. The control condition is made as similar to the experimental condition as possible, except a placebo treatment is given instead of acupuncture. The two conditions are run on separate days at the same time of day. The pain ratings in the accompanying table are obtained.
a. What is the null hypothesis?
b. Using = 0.052 tail, what is your conclusion?
c. What error might you be making by your conclusion in part c?
d. To what population does your conclusion apply?
Subject Acupuncture Placebo
1 4 6
2 2 5
3 1 5
4 5 3
5 3 6
6 2 4
7 3 7
8 2 6
9 1 8
10 4 3
11 3 7
12 4 8
13 5 3
14 2 5
15 1 4
Respond
a. The null hypothesis in this case would be that there is no significant difference in pain tolerance between the acupuncture and placebo treatments.
b. To determine the conclusion, we can perform a dependent samples t-test using the pain ratings data for both conditions. With a significance level (α) of 0.05 and a two-tailed test, we can compare the mean differences between the acupuncture and placebo treatments.
Using statistical software or a calculator, you can input the pain ratings for acupuncture and placebo treatments and perform a dependent samples t-test. The output of the test will provide a t-value and a p-value.
To interpret the result, compare the p-value to the significance level (α). If the p-value is less than α, which in this case is 0.052, we reject the null hypothesis. If the p-value is greater than or equal to α, we fail to reject the null hypothesis.
c. The error that could be made by the conclusion is a Type I error. This occurs when we reject the null hypothesis when it is actually true. In other words, we conclude that there is a significant difference in pain tolerance between the acupuncture and placebo treatments when, in reality, there is no significant difference.
d. The conclusion would apply to the population of university undergraduate volunteers from which the 15 students were randomly chosen. However, it is important to note that generalizing the results beyond this specific population might require further research and replication of the study with a larger and more diverse sample.