The following sample of lengths was taken from 9 rods off the assembly line. Construct the 99% confidence interval for the population standard deviation for all rods that come off the assembly line. Round your answers to two decimal places.

13.6,13.8,14.1,13.6,13.3,13.5,13.9, 13.3,14.1

99% confidence interval for the population standard deviation = (0.17 , 0.75).

Step-by-step explanation:

We are given that the following sample of lengths was taken from 9 rods off the assembly line;

13.6, 13.8, 14.1, 13.6, 13.3, 13.5, 13.9, 13.3, 14.1

So, firstly the pivotal quantity for 99% confidence interval for the population standard deviation is given by;

        P.Q. = ~

where, s = sample standard deviation

            = population standard deviation

           n = sample of rods = 9

Also, , where X = individual data value

                                              = mean of data values = 13.7

        = 0.094

So, 99% confidence interval for population standard deviation, is;

P(1.344 < < 21.95) = 0.99 {As the table of at 8 degree of freedom

                                              gives critical values of 1.344 & 21.95}

P(1.344 < < 21.95) = 0.99

P( < < ) = 0.99

P( < < ) = 0.99

99% confidence interval for = ( , )

                                                  = ( , )

                                                  = (0.03 , 0.56)

99% confidence interval for = ( , )

                                                 = (0.17 , 0.75)

Therefore, 99% confidence interval for the population standard deviation for all rods that come off the assembly line is (0.17 , 0.75).

y=mx+b

step-by-step explanation:

m slope, b y-intercept