When S2 is the sample variance of a normal randomsample, sn 2 1dS2ys2 has a chi-squared

Chapter 16, Problem 20

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When S2 is the sample variance of a normal randomsample, sn 2 1dS2ys2 has a chi-squared distribution withn 2 1 df, soP1x.999,n21 2 , sn 2 1dS2s2 , x.001,n21 22 5 .998from whichP1s2x.999,n21 2n 2 1, S2 , s2x.001,n21 2n 2 1 2 5 .998This suggests that an alternative chart for controllingprocess variation involves plotting the sample variancesand using the control limits LCL 5 s2x.999,n21 2 y(n 2 1) UCL 5 s2x.001,n21 2 y(n 2 1)Construct the corresponding chart for the data ofExercise 11. [Hint: The lower- and upper-tailed chi-squaredcritical values for 5 df are .210 and 20.515, respectively.]

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