# What is a 90% confidence interval for the population mean birth weight based on the data?

## An SRS of 20 recent birth records at the local hospital were selected. In the sample, the average birth weight was 121.4 ounces and the standard deviation was 7.5 ounces. I assume that in the population of all babies born in this hospital, the birth weights follow a Normal distribution, with some mean. I am also interested in a 99% confidence interval for the population mean birth weight. What is the margin of error associated with the confidence interval?

Nov 14, 2017

90% confidence interval between 118.64 ounces and 124.16 ounces

99% confidence interval between 117.13 ounces and 125.67 ounces

#### Explanation:

Given -
Mean weight $\overline{x} = 121.4$
Sample size $n = 20$
Standard Deviation $\sigma = 7.5$

Birth weight follows Normal Distribution.

Standard Error $S E = \frac{\sigma}{\sqrt{n}} = \frac{7.5}{\sqrt{20}} = \frac{7.5}{4.47} = 1.68$

Critical Value for 90% confidence $z = 1.64$

90% confidence Interval

$\mu = \overline{x} \pm z . S E$
$\mu = 121.4 \pm \left(1.64 \times 1.68\right)$
$\mu = 121.4 \pm 2.76$

With 90% confidence interval, population mean birth weight falls between 118.64 ounces and 124.16 ounces

Critical Value for 99% confidence $z = 2.54$

$\mu = \overline{x} \pm z . S E$
$\mu = 121.4 \pm \left(2.54 \times 1.68\right)$
$\mu = 121.4 \pm 4.27$

With 99% confidence interval, population mean birth weight falls between 117.13 ounces and 125.67 ounces