Question

The diameters​ (in inches) of 17 randomly selected bolts produced by a machine are listed. Use a 99​% level of confidence to construct a confidence interval for ​(a) the population variance sigma squared and ​(b) the population standard deviation sigma. Interpret the results.

4.477 4.427 4.024 4.309 4.006 3.742 3.829 3.749 4.224 3.961 4.128 4.573 3.958 3.742 3.857 3.832 4.465 ​

(a) The confidence interval for the population variance is ​(__,__​). ​(Round to three decimal places as​ needed.)

Answer 1

n = sample size = 17

s^2 = population variance = 0.070892

  

• Values of from the table at 16 degree of freedom

             = 28.845

             = 6.908

= [(17-1) * (0.070892)] / 28.8845 < S^2 < [(17-1) * (0.070892)] / 6.908

= 0.0393 < S^2 < 0.1642 answer of question a

= 0.1982 < S^2 < 0.4052 answer of question b

a) the confidence interval for the population variance is 0.1982 to 0.4052

We say that the population variance is estimated to be 0.070892. From the calculation we are 95% confident that the true population variance is between 0.0393 and 0.1642.

or