Question

A sample of 6 sewing needles is randomly selected and the following diameters are measured in millimeters. Give a point estimate for the population standard deviation. Round your answer to three decimal places. 0.95,0.99,1.04,0.95,1.05,1.05

Answer 1

Answer:

Point estimate for the population standard deviation = 0.048

Step-by-step explanation:

We are given that a sample of 6 sewing needles is randomly selected and the following diameters are measured in millimeters;

      X                             X - X bar                          $(X-Xbar)^{2}$    

    0.95                   0.95 - 1.005 = -0.055              0.003025

    0.99                   0.99 - 1.005 = -0.015               0.000225

     1.04                    1.04 - 1.005 = 0.035                0.001225

     0.95                  0.95 - 1.005 = -0.055               0.003025

     1.05                   1.05 - 1.005 = 0.045                 0.002025

     1.05                   1.05 - 1.005 = 0.045                0.002025      

                                                                            Total = 0.01155    

Firstly, mean of the data above, X bar = $\frac{\sum X}{n}$ = $\frac{6.03}{6}$ = 1.005

Standard deviation of data, S.D. = $\sqrt{\frac{\sum (X-Xbar)^{2} }{n-1} }$

                                                      = $\sqrt{\frac{0.01155}{6-1} }$ = 0.048

Therefore, point estimate for the population standard deviation is 0.048 .