Suppose I am conducting a test of significance where the null hypothesis is my cat Grayce will pick the correct cancer specimen 25% of the time and the alternate hypothesis is that she will pick the cancer specimen at a rate different than 25%. I end up with a p-value of .02. I also construct 95% and 99% confidence intervals from my data. What will be true about my confidence intervals? The answer is 95% interval will not contain .25 and the 99% interval will contain .25. How did they figure this out?