Question

The average height of students at UH from an SRS of 12 students gave a standard deviation of 3.1 feet. Construct a 95% confidence interval for the standard deviation of the height of students at UH. Assume normality for the data.

Answer 1

Answer: $(2.20,\ 5.26)$

Step-by-step explanation:

The confidence interval for the standard deviation is given by :-

$\left ( \sqrt{\dfrac{(n-1)s^2}{\chi^2_{n-1,\alpha/2}}},\ \sqrt{\dfrac{(n-1)s^2}{\chi^2_{n-1,1-\alpha/2}}} \ \right )$

Given : n= 12 ; s= 3.1

Significance level : $\alpha=1-0.95=0.05$

Using Chi-square distribution table ,

$\chi^2_{11,0.025}}=21.92\\\\\chi^2_{11,0.975}}=3.82$

Now, the 95% confidence interval for the standard deviation of the height of students at UH is given by :-

$\left ( \sqrt{\dfrac{(11)(3.1)^2}{21.92}},\ \sqrt{\dfrac{(11)(3.1)^2}{3.82}} \ \right )\\\\=\left ( 2.19602743525, 5.26049188471\right )\approx(2.20,\ 5.26)$