1. A researcher is interested in knowing about the number of hours UCF students sleep per night. In a survey of 400 UCF students, the average number of hours slept per night was 6.5 with a population standard deviation of 2 hours. a. Create a 95% confidence interval for the true number of hours slept by UCF students?

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)