For the problem we just discussed. The interval doesn’t include the number, but what if the confidence interval for that number is calculated and both confidence intervals overlap? Then they would not have convincing evidence.

It wouldn’t necessarily be appropriate to construct a confidence interval around 0.2, since it isn’t a statistical measurement. It’s just the value we expect the true proportion to be. Does that help?

Yes! Thank you! If I was trying to find a difference between means, would it then be appropriate to compare the C.I’s to see if there is an overlap?

It would be more powerful/appropriate to find the interval for the difference between means (assuming the two means are independent) and see if it contains zero than it would be to build two CIs and see if they overlap.

For this FRQ (d only). The confidence interval for 2020 doesn’t contain 8, but if the C.I for 1975 is completed they overlap. What would the correct answer be? (Sorry to insist so much I am very curious about this)

8 is not in the 95% CI so at the alpha level of 5% he has convincing evidence that the mean diameter of all aspens in the park in 2020 IS DIFFERENT from 8