A researcher claims the mean score on an agility test will go down after drinking alcohol. The mean score on the test is historically 8.6 for people not under the influence of alcohol. The researcher randomly tests 40 subjects under the influence of alcohol and finds they have a mean score of 7.3 with a standard deviation of 2.1. What test should the researcher perform to evaluate if scores are indeed lower for subjects under the influence of alcohol?
a. One-Proportion Z-Test b. Two-Proportion Z-Test c. One-Sample (Mean) T-Test d. Two-Sample (Mean) T- Test e. Matched Pairs T-Test
My Answer I picked B since there are two groups and the sample size is over 30 and we know the standard deviation
Would appreciate some feedback!
Though there are two groups (under influence of alcohol and not under influence), we are comparing the mean for the group under the influence of alcohol to a fixed number, so we want a one-sample test. If instead you took a sample of the group that wasn't under the influence of alcohol as well (instead of just reporting a fixed number), we'd want a two-sample test as you say.
We don't know the population standard deviation, so we should use the t-test. We know the standard deviation of the sample (t-test), not the population standard deviation (z-test).
Putting these two together leads to c. One-Sample (Mean) T-Test.