Question

1. Suppose a sample of 30 JJC students are given an IQ test. If the sample has a standard deviation of 12.23 points, find a 90% confidence interval for the population standard deviation.

Answer 1

Solution :

Given that,

s = 12.23

s² = 149.5729

$\chi$²_R = $\chi$ ²_{$\alpha$/2,df} = 42.557

$\chi$²_L = $\chi$ ²_{1 - $\alpha$ /2,df} = 17.708

The 90% confidence interval for $\sigma$ is,

$\sqrt$(n - 1)s² / $\chi$ ²_$\alpha$/2 < $\sigma$ < $\sqrt$ (n - 1)s² / $\chi$ ²_{1 - $\alpha$ /2}

$\sqrt$(29)(149.5729) / 42.557 < $\sigma$ < $\sqrt$ (29)(149.5729) / 17.708

10.10 < $\sigma$ < 15.65

(10.10 , 15.65)