An engineer designs an improved light bulb. The previous design had an average lifetime of 1200 hours. The new bulb had a lifetime of 1200.2 hours, using a sample of 40,000 bulbs. Although the difference is quite small, the effect was statistically significant. The most likely explanation is
A) that new designs typically have more variability than standard designs.
B) that the sample size is very large.
C) that the mean of 1200 is large.
D) All of the answer choices are very likely explanations.

Question

Quizplus · Accepted Answer

The large sample size of 40,000 bulbs increases the power of the statistical test to detect even small differences in the mean lifetime of the bulbs. This makes it more likely that the observed difference between the two designs is statistically significant, despite the fact that the practical significance of the difference is small. Option A is incorrect because there is no reason to assume that new designs have more variability than standard designs, without additional information. Option C is incorrect because the mean of 1200 is not particularly large or small in this context, and is not relevant to the statistical significance of the difference between the two designs. Option D is incorrect because it includes options that are clearly false or irrelevant.

An Engineer Designs an Improved Light Bulb