An insurance company has identified the 10 safest and the 10

An insurance company has identified the 10 safest and the 10 least-safe US cities from among the 200 largest cities in the US, based on the mean number of years drivers went between automobile accidents. They found that the cities on both lists (mentioned above) were all smaller in population size than the the 10 most highly populated cities. Use the ideas behind the sampling distribution of the mean to explain why this was expected.

Solution

When sample size increases precision also increases as a result of decreasing variability. Its growth, very sharp in the region of small samples, becomes slower and steadier beyond a certain sample size.