Chapter 9.3, Problem 107E

To determine

To find : best answer for given statement “ 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 “

Answer to Problem 107E

Option (a) is correct that is it is based on a very large random sample and a $5\%$ significance level is used.

Explanation of Solution

Given information :

1. it is based on a very large random sample and a $5\%$ significance level is used.
2. it is based on a very large random sample and a $1\%$ significance level is used.
3. it is based on a very small random sample and a $5\%$ significance level is used
4. it is based on a very small sample and a $1\%$ significance level is used.
5. the size of the sample doesn't have any effect on the significance of the test.

The best answer for the given statement is “it is based on a very large random sample and a $5\%$ significance level is used.”

Since, 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.

The larger sample size the more data one will have about the difference in life expectancy and so more reliable estimates are. Yet since there is a actually a difference in mean life expectancy it is also implies that on will likely to reject the null hypothesis and that is why it is more likely to obtain a significant increase.

So the correct option is (a).