Question

A 95% confidence interval for the mean trading achievement score for a population of third grade students is (44.2, 54 2). Suppose you compute a 99% confidence interval using the same information. Which of the following statements are correct?

The intervals have the same width
The 99 percent interval is shorter
The 99 percent interval is longer
Answer can't be determined
None of the above

Answer 1

Solution:

Answer is 99% confidence interval is longer.

We know that the confidence interval for the population mean is given by,

Observe that , as the value of    increases, the margin of the error increases and the confidence interval becomes the longer. We also know that , as the level of confidence increases , the value of   also increases .

So we can say that , as the level of confidence increases , the confidence interval becomes longer.

Answer is 99% confidence interval is longer.