A tennis player ran a simulation twice to estimate the proportion of wins to expect using a new game strategy. Each time, the simulation ran a trial of 1,000 games. The first simulation returned 172 wins, and the second simulation returned 205 wins. Construct and interpret 95% confidence intervals for the outcomes of each simulation.

The confidence interval from the first simulation is (0.149, 0.195), and the confidence interval from the second simulation is (0.180, 0.230). For the first trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.149 and 0.195. For the second trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.180 and 0.230. The confidence interval from the first simulation is (0.149, 0.195), and the confidence interval from the second simulation is (0.180, 0.230). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.149 and 0.195. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.180 and 0.230. The confidence interval from the first simulation is (0.152, 0.192), and the confidence interval from the second simulation is (0.184, 0.226). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.152 and 0.192. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.184 and 0.226. The confidence interval from the first simulation is (0.152, 0.192), and the confidence interval from the second simulation is (0.184, 0.226). For the first trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.152 and 0.192. For the second trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.184 and 0.226.