Question

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 alternative hypothesis is that she will pick the cancer specimen at a rate different than 25%. I end up with a p-value of 0.02. I also construct 95% and 99% confidence intervals from my data. What will be true about my confidence intervals?

Answer 1

Neither the 95% nor the 99% intervals will contain 0.25.

Explanation:

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 alternative hypothesis is that she will pick the cancer specimen at a rate different than 25%. I end up with a p-value of 0.02. I also construct 95% and 99% confidence intervals from my data then neither the 95% nor the 99% intervals will contain 0.25.