A chess 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 212 wins, and the second simulation returned 235 wins. Construct and interpret 95% confidence intervals for the outcomes of each simulation.

A: The confidence interval from the first simulation is (0.187, 0.237), and the confidence interval from the second simulation is (0.209, 0.261). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.187 and 0.237. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.209 and 0.261.

B: The confidence interval from the first simulation is (0.187, 0.237), and the confidence interval from the second simulation is (0.209, 0.261). For the first trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.187 and 0.237. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.209 and 0.261.

C: The confidence interval from the first simulation is (0.191, 0.233), and the confidence interval from the second simulation is (0.213, 0.257). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.191 and 0.233. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.213 and 0.257.

D: The confidence interval from the first simulation is (0.191, 0.233) and the confidence interval from the second simulation is (0.213, 0.257). For the first trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.191 and 0.233. For the second trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.213 and 0.257.