Question

Assume that the heights of bookcases are normally distributed. A random sample of 16 bookcases in one company have a mean height of 67.5 inches and a standard deviation of 3.6 inches. Construct a 99% confidence interval for the population standard deviation, σ.

Answer 1

Answer: 1.1 and 3.1

Step-by-step explanation:

Answer 2

Answer:  $2.43$

Step-by-step explanation:

Given :  Confidence level :$1-\alpha=0.99$

Significance level :$\alpha=0.01$

Sample size : n= 16

Sample standard deviation : s= 3.6 inches

Using chi-square distribution table , the critical values are:

$\chi^2_{\alpha/2, n-1}=\chi^2_{0.005, 15}=32.80132065\\\\\chi^2_{1-\alpha/2, n-1}=\chi^2_{0.995, 15}=4.60091557$

We know that , confidence interval for the population standard deviation is given by :-  

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

Hence ,  a 99% confidence interval for the population standard deviation is $2.43$.