An experiment will be conducted to test the effectiveness of a weight-loss supplement. Volunteers will berandomly assigned to take either the supplement or a placebo for 90 days, with 12 volunteers in each group. Thesubjects will not know which treatment they receive. At the end of the experiment, researchers plan to calculatethe mean weight loss for each of the two groups and to construct a two-sample t-confidence interval for thedifference of the two treatment means. Which of the following assumptions is necessary for the confidenceinterval to be valid?(A) The sample size is greater than or equal to 10 percent of the population size.(B) Each of the two groups has at least 5 successes and at least 5 failures.(C) The distributions of weight loss of the two treatments are approximately normally distributed.(D) The volunteers in the supplement group are paired with volunteers in the placebo group.(E) The expected number of people who lose weight in each group is at least 5.
Question
An experiment will be conducted to test the effectiveness of a weight-loss supplement. Volunteers will berandomly assigned to take either the supplement or a placebo for 90 days, with 12 volunteers in each group. Thesubjects will not know which treatment they receive. At the end of the experiment, researchers plan to calculatethe mean weight loss for each of the two groups and to construct a two-sample t-confidence interval for thedifference of the two treatment means. Which of the following assumptions is necessary for the confidenceinterval to be valid?(A) The sample size is greater than or equal to 10 percent of the population size.(B) Each of the two groups has at least 5 successes and at least 5 failures.(C) The distributions of weight loss of the two treatments are approximately normally distributed.(D) The volunteers in the supplement group are paired with volunteers in the placebo group.(E) The expected number of people who lose weight in each group is at least 5.
Solution
The correct answer is (C) The distributions of weight loss of the two treatments are approximately normally distributed.
This is because the t-test (which is used to construct the confidence interval) assumes that the data comes from a normal distribution. This assumption is necessary to ensure the validity of the test results. If the data is not normally distributed, the test results may not be accurate.
The other options are not necessary assumptions for a t-test. For example, the sample size does not need to be greater than or equal to 10 percent of the population size (A), and there is no requirement for a minimum number of successes or failures (B). Similarly, there is no need for the volunteers to be paired (D), and there is no requirement for a minimum number of people who lose weight in each group (E).
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