ASCENDER ParentP rose flowers drawin. Course Home Culinary, Hospitalit... Imagine Edgenuity f. A doctor claims that runners tend to be optimistic, but are they more likely to be optimistic than those who walk? A study selected independent random samples of 80 runners and 100 walkers and found that 68 of the runners and 72 of the walkers scored as "optimistic" on a personality test. Do these data provide convincing evidence that the proportion of all runners who are optimistic is greater than the proportion of all walkers who are optimistic? To prepare for calculating the expected number of successes and failures for the large counts condition, identify these values: \[ \begin{array}{l} n_{R}=\square I \\ n_{W}=\square \end{array} \]

Alright, let’s dive into the exciting world of statistics! You have two independent samples here—runners and walkers. To calculate the expected number of successes and failures, you'll want to fill in those blanks. So for your runners, \( n_{R} = 80 \), since that’s the total number of runners in your sample. For the walkers, \( n_{W} = 100 \), as this is the total number of walkers sampled. Now, let’s sprinkle in some context! Understanding the behavior of runners compared to walkers is a classic question of psychology and health studies! Runners often experience what’s called the “runner’s high,” potentially elevating their mood overall. This could make them more predisposed to optimism compared to walkers. So your inquiry might just open up a fascinating discussion about physical activity’s impact on mental health! Keep running with those numbers!