Question

A student randomly selects 16 DVD’s at a store. The prices of the DVD’s have a standard deviation of $2.25.

Construct a 95% confidence interval for the population standard deviation. Assume the data are normally distributed.

Answer 1

Solution :

Given that,

s = 2.25

s2 = 5.0625

$\chi$2R = $\chi$ 2$\alpha$/2,df = 27.488

$\chi$2L = $\chi$ 21 - $\alpha$ /2,df = 6.262

The 95% confidence interval for $\sigma$ is,

$\sqrt$(n - 1)s2 / $\chi$ 2$\alpha$/2 < $\sigma$ < $\sqrt$ (n - 1)s2 / $\chi$ 21 - $\alpha$ /2

$\sqrt$(15)(5.0625) / 27.488 < $\sigma$ < $\sqrt$ (15)(5.0625) / 6.262

1.66 < $\sigma$ < 3.48

(1.66 , 3.48)