# A study of one thousand teens found that the number of hours they spend on social networking sites each week normally distributed with a mean of 15 hours. The population standard deviation is 2 hours. What is the 95% confidence interval for the mean?

Sep 6, 2016

Population Mean lies between $15.0294$ and $14.9706$

#### Explanation:

Given -

Sample Mean $\overline{x} = 15$
Sample size $n = 1000$
Population SD $\sigma = 2$
Confidence interval = 95%

Population Mean $\mu = \overline{x} \pm \left(z \times S E\right)$

$S E \to$ Standard Error

$S E = \frac{\sigma}{\sqrt{n}} = \frac{15}{1000} = 0.015$

Critical Value of $z$ for 95% confidence interval $= 1.96$

$\mu = 15 \pm \left(1.96 \times 0.015\right)$
$\mu = 15 \pm 0.0294$

Upper Limit

$\mu = 15 + 0.0294 = 15.0294$

Lower Limit

$\mu = 15 - 0.0294 = 14.9706$