8
QuizMultiple Choice
Scope of Inference
Question 8 of 10 • VA-Probability and Statistics
A consumer agency wants to determine which of two laundry detergents, A or B, cleans better. Fifty pieces of fabric are subjected to the same kinds of stains (grass, mud, coffee). Then 25 pieces are randomly assigned to be cleaned with detergent A, and the remaining 25 pieces are cleaned with detergent B. After being laundered, the pieces of fabric are rated on a scale from 1–10, with 1 being the least clean to 10 being the most clean. The difference in mean ratings (A – B) was determined to be –2.3. Assuming there is no difference in the two detergents, 200 simulated differences in sample means are displayed in the dotplot.Using the dotplot and the difference in mean ratings from the samples, is there convincing evidence that the one detergent is better than the other?
Answer
A
Yes, because a difference in mean rating of –2.3 or less occurred only 5 out of 200 times, meaning the difference is statistically significant, and there is convincing evidence that A is more effective than B.B
Yes, because a difference in mean rating of –2.3 or less occurred only 5 out of 200 times, meaning the difference is statistically significant, and there is convincing evidence that B is more effective than A.C
No, because a difference in mean rating of –2.3 or more occurred 195 out of 200 times, meaning the difference is not statistically significant, and there is not convincing evidence that one brand is better than the other.D
No, because a difference in mean rating of –2.3 or less only occurred 5 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.