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.

Step-by-step explanation:

The formula to find the confidence interval for mean :

$\overline{x}\pm z_c\dfrac{\sigma}{\sqrt{n}}$ , 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 .