Answer: (6.304, 6.696)
Step-by-step explanation:
The confidence interval for population mean is given by :-
[tex]\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}[/tex]
, where [tex]\sigma[/tex] = Population standard deviation.
n= sample size
[tex]\overline{x}[/tex] = Sample mean
z* = Critical z-value .
Let x denotes the number of hours slept by UCF students.
Given : [tex]\sigma=2\ hours[/tex]
n= 400
[tex]\overline{x}= 6.5\ hours[/tex]
Two-tailed critical value for 95% confidence interval = [tex]z^*=1.96[/tex]
Then, the 95%confidence interval for the true number of hours slept by UCF students will be :-
[tex]6.5\pm(1.96)\dfrac{2}{\sqrt{400}}\\\\=6.5\pm(1.96)\dfrac{2}{20}\\\\=6.5\pm0.196=(6.5-0.196,\ 6.5+0.196)=(6.304,\ 6.696)[/tex]
Hence, the 95% confidence interval for the true number of hours slept by UCF students : (6.304, 6.696)
