To find the standard deviation of the diameter of wooden dowels, the manufacters measures 19 randomly selected dowels and finds the standard deviation of the sample to be s= 0.16. Find the 95% CI for the population standard deviation σ

Step 1:

The number of samples are 19.

The point estimate for standard deviation is s = 0.16.

Confidence level is 95%.

Find the 95% confidence interval for the standard deviation.

Confidence interval for standard deviation is .

Where n is number of samples,

            are critical values correspond to the given level of confidence.

Step 2:

Now find the critical values .

Area to the right of .

Area to the left of .

Use the Chi-square distribution table to find the critical values.

Step 3:

Substitute ,  in Confidence interval.

Therefore the 95% confidence interval for the standard deviation is .

Solution :

The 95% confidence interval for the standard deviation is .