# If a data set of n=115 has a mean of 9.74 and a population standard deviation of 2.93, what is the 95% confidence interval?

Nov 2, 2015

We are 95% confidence that the population mean lies between $10.27$ and $9.21$

#### Explanation:

95% Confidence interval is -

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

$S E = \frac{\sigma}{\sqrt{n}} = \frac{2.93}{\sqrt{115}} = \frac{2.93}{10.72} = 0.27$

$z$ value for 95% confidence

$z = 1.96$

Upper Limit:

$\mu = 9.74 + \left(0.27 \times 1.96\right)$
$\mu = 9.74 + 0.53$
$\mu = 10.27$

Lower Limit:

$\mu = 9.74 - \left(0.27 \times 1.96\right)$
$\mu = 9.74 - 0.53$
$\mu = 9.21$