The latest in the "You may be a redneck if . . . " genre has produced a simple questionnaire. If more than 80% of the questions are answered in accordance with redneck"philosophy" (e.g., "You may be a redneck if grade 4 was the best 5 years of your life") the test declares the respondent a redneck, but otherwise assumes that variation in the percentage of answers scored as redneck (including scores over 80%) is to be expected in people not actually rednecks. From that perspective, describe with reference to the test
(a) what corresponds to the criterion of the test?
(b) what would be a Type I error for the test?
(c) what would constitute a Type II error for the test? (d) what would correspond to the power of the test?
(a) The criterion of the test in this case is the percentage of questions answered in accordance with redneck philosophy. If more than 80% of the questions are answered in line with redneck beliefs, the test declares the respondent a redneck.
(b) Type I error for this test would occur when someone who is not actually a redneck (i.e., does not align with redneck philosophy) answers more than 80% of the questions in accordance with redneck beliefs, but is still declared a redneck by the test.
(c) Type II error for this test would occur when someone who is actually a redneck (i.e., aligns with redneck philosophy) answers less than 80% of the questions in accordance with redneck beliefs, but is not declared a redneck by the test.
(d) The power of the test in this case refers to its ability to correctly identify those who are actually rednecks (i.e., correctly declare them as rednecks based on their responses). A high power would mean that the test has a high chance of correctly identifying rednecks, while a low power would indicate a higher likelihood of false negatives (i.e., not correctly identifying rednecks).