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�r <br /> ORDP 20-110 ANALYSIS OF MEASUREMENT DATA <br /> 3-3.2 DOES THE AVERAGE OF PRODUCT A EXCEED THE AVERAGE OF PRODUCT Bt <br /> 3-3.2.1 (Case 1)—Variability of A and 8 is Unknown, but can be Assumed to be Equal. <br /> Data Sample 34.2.1--Surface Hardness of Steel Plates <br /> A study was made of the effect of two grinding conditions on the surface hardness of steel plates <br /> used for intaglio printing. Condition A represents surfaces "as ground"and Condition B re <br /> presents <br /> surfaces after light polishing with emery paper. The observations are hardness indentation numbers. <br /> Condition A Condition B <br /> 187 157 <br /> 157 152 <br /> 152 148 <br /> 164 158 <br /> 159 161 <br /> 164 <br /> 172 <br /> (One-sided t4estj <br /> Procedure Example <br /> (1) Choose a. the significance level of the test. (1) Let a - .05 <br /> (2) Look up 4-. for . - n,, + n, - 2 degrees (2) nA - 7 <br /> of freedom in Table A-4. nit - 5 <br /> r - 10 <br /> t.,,for 10 U. - 1.812 <br /> (3) Compute: $A and dA, to and s±. from the (3) ZA - 165 <br /> nA and no measurements from products A sA - 134 <br /> and B, respectively. to - 155.2 <br /> (4) Compute (4) 81 - 26.7 <br /> sP - _1(nA - 1)s'A + (no - 1)sr. f 6(134) +4(26.7) <br /> 11 nA +n8 - 2 s� - �f <br /> 10 <br /> - <br /> (5) Compute (5) = 9.544 <br /> u — tt-.sp nA + ns <br /> (1.812) (9.544)J12 <br /> 35 <br /> = 17.294(.5855) <br /> - 10.1 <br /> (6) If(XA - to) > u,decide that the average (6) (ZA - $o) = 9.8,which is not larger than <br /> of A exceeds the average of B; otherwise, u. There is no reason to believe that the <br /> decide there is no reason to believe that the average hardness for Condition A exceeds <br /> average of A exceeds the average of B. the average hardness for Condition B. <br /> (7) Let MA and fns be the true averages of A (7) ($A - lo) - u - 9.8 - 10.1 - -0.3. <br /> and B. Note that the interval from The interval from -0.3 to - is a 95%one- <br /> ((tA - t/) - ul to m is a 1 - a one sided confidence interval estimate of the <br /> sided confidence interval estimate of the true difference between averages. <br /> true difference (MA - me). <br /> 3-34 <br />