Question

Rivet holes are punched in steel beams. To ensure that the rivets will fit and that the joint will have adequate strength, it is necessary to control the standard deviation o the diameter, and measurements are made periodically. Ten measurements are made of nominally 1-inch-diameter holes, and the standard deviation is found to be 0.002 inches. What is the 95% confidence interval on the standard deviation? Required – confidence interval in the standard deviation → Chi-squared distribution. S = 0,002 in., n = 10,  = n – 1 = 9. 95% confidence level:  = 1-0.95 = 0.05.

Answer 1

The 95% confidence interval for the standard deviation of the diameter is (0.0014; 0.0036).

Explanation:

We have to calculate a confidence interval for the standard deviation.

The confidence level is 95%.

The size of the sample is n=10.

The sample standard deviation is s=0.002.

The lower limit is calculated as:

`LL=s\sqrt{(n-1)/(\chi_((1-\alpha)/2;n-1))}\\\\\\LL=0.002\sqrt{(10-1)/(19.02)}=0.002√(0.473)=0.002*0.688=0.0014`

`UL=s\sqrt{(n-1)/(\chi_(\alpha/2;n-1))}\\\\\\UL=0.002\sqrt{(9)/(2.7)}=0.002√(3.33)=0.002*1.826=0.0036`

The 95% confidence interval for the standard deviation of the diameter is (0.0014; 0.0036).