Vigorous exercise helps people live several years longer (on 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 expectancy if

(a) it is based on a very large random sample and a 5% significance level is used.

(b) it is based on a very large random sample and a 1% significance level is used.

(c) it is based on a very small random sample and a 5% significance level is used.

(d) it is based on a very small random sample and a 1% significance level is used.

(e) the size of the sample doesn't have any effect on the significance of the test.

The life expectancy of the typical time a life form is supposed to live, in light of the extended period of its introduction to the world, its ongoing age, and other segment factors like sex.

As, vigorous exercise leads to living several extra on average and as regular slow walking leads to living $2$months extra on average, there will be a difference in the mean life expectancy between those who do vigorous exercise and those who does regular slow walking.

When the sample size with a higher significance level is greater, the mean life expectancy significance increases.

Hence a statistical test is more likely to find a significant increase in mean life expectancy if it is based on a very large random sample and a $5\%$significance level is used.

Hence, the correct option is (a).