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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

asked Apr 17, 2015 in STATISTICS by doan12345 Pupil
reshown Apr 18, 2015 by bradely

1 Answer

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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 image.

Where n is number of samples,

            image are critical values correspond to the given level of confidence.

Step 2:

Now find the critical values image.

Area to the right of image .

Area to the left of image .

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

image

image

Step 3:

Substitute imageimage in Confidence interval.

image

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

Solution :

The 95% confidence interval for the standard deviation is image.

answered Apr 18, 2015 by yamin_math Mentor

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