Question

The National Center for Education Statistics surveyed 4400 college graduates about the lengths of time

required to earn their bachelor’s degrees. The mean was 5.15 years and the standard deviation was 1.68

years. Based on the above information, construct a 95% confidence interval for the mean time required to

earn a bachelor’s degree by all college students.

The confidence level is ________________%

 

Answer 1

$n=4400, \mu=5.15 \text{ years }, \sigma=1.68 \text{ years}$

$\alpha=0.05,\dfrac{\alpha}{2}=0.025$

$Z_{\frac{\alpha}{2}}=Z_{0.025}=1.96$

95% confidence level is given by-

$=\mu\pm Z_{0.025}\dfrac{\sigma}{\sqrt{n}}$

$=5.15\pm 1.96\times \dfrac{1.68}{\sqrt{4400}}$

$=5.15\pm 0.0496$

$=(5.10,5.1996)$

Hence 95% confidence level is (5.10,5.1996)