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Question

Use the given degree of confidence and sample data to find CI for the population standard deviation σ. Assume that the population has a normal distribution. Round the confidence interval limits to the same number of decimal places as the sample standard deviation.

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

Answer 1

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 .