Sampling and Experimentation — Test

Question 18 • Statistics and Probability

Using this dotplot and the difference in proportions from the samples, is there convincing evidence that the new additive was more effective?

Answer

Yes, because a difference in proportions of 0 point 4 or less occurred 193 out of 200 times, meaning the difference is statistically significant and the new additive is more effective.

No, because a difference in proportions of 0 point 4 or less occurred 193 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective.

No, because a difference in proportions of 0 point 4 or more occurred 7 out of times, meaning the difference is not statistically significant and the new additive is not more effective.

Yes, because a difference in proportions of 0 point 4 or more occurred 7 out of 200 times, meaning the difference is statistically significant and the new additive is more effective.

Explanation

The observed difference in sample proportions is 0.4. The dotplot shows that a difference of 0.4 or more occurred in 7 of 200 simulated samples, or 7/200 = 0.035 (3.5%). Because this is a small proportion of the simulations, the result is statistically significant at the 5% level, giving convincing evidence that the new additive was more effective.

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