To find the standard deviation of the diameter of wooden dowels, the manufacturer measures 19 randomly selected dowels and finds the standard deviation of the sample to be sequals0.16. find the 95% confidence interval for the population standard deviation sigma. round to two decimal places.
a. 0.13less thansigmaless than0.22
b. 0.15less thansigmaless than0.21
c. 0.11less thansigmaless than0.25
d. 0.12less thansigmaless than0.24

Option D -  

Step-by-step explanation:

Given : The manufacturer measures 19 randomly selected dowels and finds the standard deviation of the sample to be s=0.16.

To find : The 95% confidence interval for the population standard deviation sigma?

Solution :

Number of sample n=19

The degree of freedom is Df=n-1=19-1=18

The standard deviation of the sample is s=0.16

Applying chi-square table to find critical value,

Upper critical value of is

Lower critical value of is  

Lower limit of the 95% confidence interval for the population variance

Upper limit of the 95% confidence interval for the population variance

So, The 95% confidence interval for the population variance is [0.0146, 0.0560]

Now, The 95% confidence interval for the population standard deviation is

or  

Therefore, Option D is correct.

The 95% confidence interval for the population standard deviation is