Vigorous exercise helps people live several years longer (on the average). Whether mild activities like slow walking extend life is not clear. Suppose that the added life expectancy from regular slow walking is just 2 months. A statistical test is more likely to find a significant increase in mean life if
(a) it is based on a very large random sample.
(b) it is based on a very small random sample.
(c) The size of the sample doesn't have any effect on the significance of the test.