Suppose we are constructing a confidence interval using repeated tests of significance to develop an interval of plausible values. Using two-sided tests each time with the following null hypotheses, we obtain the resulting p-values. Null p-value Null p-value Proportion = 0.45 0.014 Proportion = 0.53 0.787 Proportion = 0.46 | 0.032 Proportion = 0.54|0.572 Proportion = 0.47 0.062 Proportion = 0.55 0.373 Proportion = 0.48 0.126 Proportion = 0.56 | 0.142 Proportion = 0.49 0.371 Proportion = 0.57 0.077 Proportion = 0.50 0.598 Proportion = 0.58 0.042 Proportion = 0.51 0.733 Proportion = 0.59 0.021 Proportion = 0.52 0.986 Proportion = 0.60 0.003