Question

A 95% 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.

Answer 1

Answer: b. The 99% interval is longer.

Explanation:

The formula to find the confidence interval for mean :

`\overline{x}\pm z_c(\sigma)/(√(n))` , where
`\overline{x}` is the sample mean ,
`\sigma` is the population standard deviation , n is the sample size and
`z_c` is the two-tailed test value for z.

For 95% confidence interval the two-tailed test value for z is
`z_c=1.96\approx2`.

For 99% confidence interval the two-tailed test value for z is
`z_c=2.576\approx3`.

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 .