Question

Suppose you calculate a 95% confidence interval for the difference in population means. The confidence interval contains both negative and positive values.

Will a 99% confidence interval based on the same data contain both negative and positive numbers as well? Choose the correct response from the options provided below.

Yes. Keeping all other values the same, increasing the confidence level leads to a wider interval which would still include negative and positive numbers.

No. Increasing the confidence level leads to a narrower interval so we cannot be sure if the interval would still contain both negative and positive numbers.

Yes. All 99% confidence intervals for the difference in populations means contain both negative and positive numbers, no matter the situation.

Not necessarily. We cannot be sure how changing the confidence level will affect the confidence interval.

Answer 1

The correct answer is A.

Yes. Keeping all other values the same, increasing the confidence level leads to a wider interval which would still include negative and positive numbers.

Because, 95% confidence intervals have the property that they come from a procedure that has a 95% chance of yielding an interval that contains the true value. And if we assume 99% confidence interval, then it yeild 99% true value. Hence 99% confidence interval is widen on both negative and positive sides.