Answer :
We are given that the study sampled 80 runners and 100 walkers. Therefore, the sample sizes we need for the large counts condition are
[tex]$$
n_R = 80 \quad \text{and} \quad n_W = 100.
$$[/tex]
To elaborate:
1. For runners, the study selected 80 independent subjects, so the sample size for runners is
[tex]$$n_R = 80.$$[/tex]
2. For walkers, the study selected 100 independent subjects, so the sample size for walkers is
[tex]$$n_W = 100.$$[/tex]
These values are used later in the analysis to check that the expected counts for successes (optimism) and failures (non-optimism) are sufficiently large, which is a necessary condition for using large-sample approximations in hypothesis testing.
[tex]$$
n_R = 80 \quad \text{and} \quad n_W = 100.
$$[/tex]
To elaborate:
1. For runners, the study selected 80 independent subjects, so the sample size for runners is
[tex]$$n_R = 80.$$[/tex]
2. For walkers, the study selected 100 independent subjects, so the sample size for walkers is
[tex]$$n_W = 100.$$[/tex]
These values are used later in the analysis to check that the expected counts for successes (optimism) and failures (non-optimism) are sufficiently large, which is a necessary condition for using large-sample approximations in hypothesis testing.