A college surveys a sample of 116 of its students to determine whether they would prefer a final exam or a final paper. Out of the 116 students surveyed, 41 stated that they prefer the final exam.

Question

Based on this sample data, construct a 95% confidence interval for the proportion of all students who would prefer a final exam over a final paper, and interpret this confidence interval. Assume all conditions are met, and round values to three decimal places.
95% confidence interval: (0.239, 0.468)
Interpretation: We are 95% confident that the true proportion of all students who would prefer a final exam is between 23.9% and 46.8%.
95% confidence interval: (0.239, 0.468)
Interpretation: We are confident that 95% of the time, the true proportion of all students who would prefer a final exam is between 23.9% and 46.8%.
95% confidence interval: (0.266, 0.440)
Interpretation: We are confident that 95% of the time, the true proportion of all students who would prefer a final exam is between 26.6% and 44.0%.
95% confidence interval: (0.266, 0.440)
Interpretation: We are 95% confident that the true proportion of all students who would prefer a final exam is between 26.6% and 44.0%.
95% confidence interval: (0.280, 0.426)
Interpretation: We are 95% confident that the true proportion of all students who would prefer a final exam is between 28.0% and 42.6%.

Answer 1

95% confidence interval: (0.280, 0.426)
Interpretation: We are 95% confident that the true proportion of all students who would prefer a final exam is between 28.0% and 42.6%.