Sampling and Experimentation — Test

Question 20 • Statistics

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

Answer

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.

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.

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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