Scope of Inference — Quiz

Question 5 • Statistics

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

No, because a difference in mean rating of negative 2 point 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.

No, because a difference in mean rating of negative 2 point 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.

Yes, because a difference in mean rating of negative 2 point 3 or less occurred only 5 out of 200 times, meaning the difference is statistically significant, and there is convincing evidence that cap b is more effective than cap A .

Explanation

Only 5 of the 200 simulated differences were −2.3 or smaller, so results this extreme would be rare if the detergents were equally effective. That provides convincing evidence of a statistically significant difference. Since the observed difference is negative, cap B had the higher mean rating than cap A, so cap B appears more effective.

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