Question

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 1

Answer: (6.304, 6.696)  

Step-by-step explanation:

The confidence interval for population mean is given by :-

$\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}$

, where $\sigma$ = Population standard deviation.

n= sample size

$\overline{x}$ = Sample mean

z* = Critical z-value .

Let x denotes the number of  hours slept by UCF students.

Given :  $\sigma=2\ hours$

n= 400

$\overline{x}= 6.5\ hours$

Two-tailed critical value for 95% confidence interval = $z^*=1.96$

Then, the 95%confidence interval for the true number of hours slept by UCF students will be :-

$6.5\pm(1.96)\dfrac{2}{\sqrt{400}}\\\\=6.5\pm(1.96)\dfrac{2}{20}\\\\=6.5\pm0.196=(6.5-0.196,\ 6.5+0.196)=(6.304,\ 6.696)$

Hence, the 95% confidence interval for the true number of hours slept by UCF students : (6.304, 6.696)