A95% confidence interval for the mean reading 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 is correct? a. the intervals have the same width. b. the 99% interval is longer. c. the 99% interval is shorter. d. none of the above.

b. The 99% interval is longer.

Step-by-step explanation:

The formula to find the confidence interval for mean :

, where is the sample mean , is the population standard deviation , n is the sample size and is the two-tailed test value for z.

For 95% confidence interval the two-tailed test value for z is .

For 99% confidence interval the two-tailed test value for z is .

Since the interval is directly proportion al to the z-value , so it is clear that the width of the interval would be longer with z =3 than z=2.

i.e. The 99% interval is longer than 95% confidence interval .