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 significance test is more likely to find a significant increase in mean life expectancy with regular slow walking if

Step 2: Explanation

a. It uses a $5\%$ significance level and is based on a very large random sample.

b. It is based on a very large random sample with a significance level of one percent.

c. It uses a $5\%$ significance level and is based on a very small random sample.

d. It is based on a very small random sample with a significance level of one percent.

e. The number of people in the sample has no bearing on the test's significance.

"It is based on a very big random sample and a significance level is applied," is the best response to the supplied statement.

There will be a difference in the mean life expectancy between individuals who perform strenuous exercise and those who do regular slow-walking since vigorous exercise leads to living several months longer on average and regular slow-walking leads to living months longer on average.

The higher the sample size, the more data regarding the difference in life expectancy will be available, and the more valid the estimates will be. However, because there is a difference in mean life expectancy, one will very certainly reject the null hypothesis, implying that a considerable increase is more plausible. So the correct option is (a).