Question

14 multiple choice 1 point an engineer has designed an improved light bulb. the previous design had an average lifetime of 1200 hours. based on a sample of 2000 of these new was found to be 1201 hours. although the difference is quite small, the effect was statistically significant. what is the best explanation? the mean of 1200 is large. the relative improvement in average lifetime is 0.000083, which is much smaller than 0.05. new designs typically have more variability than standard designs. the sample size is very large, so that even a small difference can be detected.

Explanation:

To determine the best explanation for the statistically significant effect despite a small difference, we analyze each option:

• Option 1: The size of the mean (1200) doesn't directly explain statistical significance; it's about the difference relative to variability and sample size. Eliminate.
• Option 2: A small relative improvement (0.000083) being smaller than 0.05 doesn't explain significance (0.05 is a common alpha level, but a small relative improvement doesn't mean significance can't occur with large sample sizes). Eliminate.
• Option 3: Variability of new vs. standard designs isn't relevant to why a small difference is significant here. Eliminate.
• Option 4: With a very large sample size (2000), the standard error (which depends on sample size) becomes small. This means even a small difference (1201 - 1200 = 1 hour) can be detected as statistically significant because the large sample increases the power of the test to detect small effects. This matches the scenario.

Answer:

The sample size is very large, so that even a small difference can be detected.