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Times New Roman1Symbol1.Times New Roman1.Times New Roman"$"#,##0_);\("$"#,##0\)!"$"#,##0_);[Red]\("$"#,##0\)""$"#,##0.00_);\("$"#,##0.00\)'""$"#,##0.00_);[Red]\("$"#,##0.00\)7*2_("$"* #,##0_);_("$"* \(#,##0\);_("$"* "-"_);_(@_).))_(* #,##0_);_(* \(#,##0\);_(* "-"_);_(@_)?,:_("$"* #,##0.00_);_("$"* \(#,##0.00\);_("$"* "-"??_);_(@_)6+1_(* #,##0.00_);_(* \(#,##0.00\);_(* "-"??_);_(@_) 0.00000 0.0000 0.0000.00.000000000000000000.0000000000000000000.00000000000000000000.000000000000000000000.0000000000000000000000.00000000000000000.0000000000000000.000000000000000.00000000000000.000000000000 0.00000000000 0.0000000000 0.000000000 0.00000000 0.0000000 0.0000000.0000000000000000000000 .00%                + ) , *      " "8!@ @ "8!@ @ "8!!@ @ "'Gic{xdf_ 96<͕oȋWC G;m^QD\55ȶ:rj#}-t  5h8;8a mU؄?%To=r y +;t{NIz[iS$$IH;_كU:t|3C:Ͳ-6ZWg;oqߩ.ϯm6І]bx Os:s|ӹ #XO/DZB~桅Z6QIv˾z~u3'zv;=a@~F,apq7O@"ř4eE֐;z@=ř4eE֐;z"RxT?hQ&&imL$BR(#ڡB-6ЯY䛤`puupP]Bkk޻/$qw>EDQݎAƩKoMB }z(h`{)H!=}Չk.|zfwg Kl8#CZ)AJ\.b~Uh$4He>~Zh, QASw{ϻl쓺D%:{d-[ xyZg+NZ]X?XT&ץhAo֛Q(j6GʼSi}FިTLF"W@s{E9Ŗ)! ֦y (|3r7 ./˙\] |R6-S*T,MC:%ZnVO(CICv'=ppyz v2K~oU~Ki]%JRɡc-M>$1{b9d=8M؀3ۏ|q߆܀I.bd~}w,5̆]g5v~XuŞfѾy$Vgo7^veѿ>Ϸ![7|zɹG}x~n^O?| b)bv?3  @@  R(mm)(in)Outer Dia. (Do)Mass (m)(g)(oz)Date: Measurement Thickness (T)English System SI SystemDiameterInches ToleranceWeightOuncesUnitsRebound*G* Freefall from 70 inches to a hard wood floor at 68 degrees Fahrenheitcmg ParameterUSHA Handball Specifications Engineer:%%%%%%%%%%%%%%%%%%%%%%%7Ball Dimension and Mass Measurements for Nine HandballsBall #USHA Handball MeasurementsData Set Descriptive StatisticsStandard Dev.:Mean:Count:RemarksS(Do(mm)-25.4*Do(in))2 =  = S(T(mm)-25.4*T(in))2  S(Do(mm)-Davg(mm))2 =   Ball_4_Mean = Ball_7_Mean == S(T(mm)-*Tavg(mm))2 = Ball_4_T_Mean= Ball_7_T_MeanN =Sample Std. Dev. = Sample Mean =(From table) t = \ reject values outside;Chauvenet s criterion would reject the one value of 9.71 mmmmqExperimental Error Analysis - Examine the original data set, reject identifiable errors and calculate uncertaintySample Standard Deviation =UOD =Table t95% value = Outside Diameter =t95__value*Std_Dev/SQRT(N)#Laboratory Measurement InstructionsNamed cell "Std_Dev"Named cell "N"Named cell "t95_value"This measurement shows an identifiable, systematic measurement error in outside diameter and thickness. The caliper was not zeroed. The offset is unknown, so this error cannot be corrected. Therefore, omit this data.yThe variability between the English and SI system measurements for both the outer diameter and the thickness for this particular ball is consistently low. This indicates the experimenter converted one measurement to the other system, and the measurements are not independent. Both values should not be included in the data set. See the variability calculations to the right.8Outer Diameter Variability Between Eng & SI Measurements3Thickness Variability Between Eng & SI MeasurementsDigital Caliper SMU:LOuter Diameter Random Uncertainty, 95% confidence interval (mm measurement):IOuter Diameter SMU Uncertainty, 95% confidence interval (mm measurement):Table t95% value = UODsmu = UODrand ==MAX(UODsmu,UODrand)LThe variability between the English and SI system measurements for both the outer diameter and the thickness for this particular ball is of the same magnitude at that among measurements. This indicates the English and SI system measurements were independent as opposed to Ball No. 4. See the variability calculations to the right.#New Sample Statistics Omitting 9.71bNote that the sample mean did not change much, but the standard deviation decreased significantly.n = 1-1/(2n) =i.e. the rangeII. Weigh one of the balls out of the sample of 12. Then measure the ball dimensions, cutting the ball open as necessary to obtain thickness measurements. Measure several different axes on the ball. Six are suggested on the Lab1 Measurements sheet. One person on the team is to make SI measurements of the ball (use the Acculab scale set to grams and Fowler Sylvac calipers set to mm) and the other person is to make English system measurements of the ball (use the Acculab scale set to ounces and Chinese manufactured dial calipers).MRaw Data and the associated error analysis are shown on subsequent worksheetsHUnited States Handball Association Specifications for Standard Handballs8Note: Observe that the various experimental groups, one for each ball, interpreted the Laboratory Measurement Instructions (given above) in a variety of ways, some correctly and some incorrectly. For example the team measuring Ball No. 2 did not take any English system measurements, which were required in the instructions. The team measuring Ball No. 11 interpreted "several different axes on the ball" to be 24 axes. While this is technically correct, there is a diminishing returns for making additional measurements, and this is probably excessive. It is necessary to understand the experimental objectives and context and environment under which the data set was collected to properly evaluate its suitability. See the comments on the Error Analysis Worksheet concerning Ball No. 4 as an example of this concept.1.96*Digital_Caliper_SMU/2This ball was carefully checked, and it is too light to be a standard USHA handball (See the USHA Specs worksheet). Depending on the final use of the data, this data may or may not be included in the data set.One thickness measurement appears to be an outlier. It is very possible that the 9 and 7 were transposed. 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If the English system measurements are independent measurements (in other words they are distinct measurements and not simply a unit conversion through the electronics of the digital caliper), they can be converted to the SI system and included in establishing the mean and uncertainty for this parameter. This may decrease the uncertainty as the number of samples increases.< L Q U    Hv GpHM+@  O]`v$ 7 <8Look up the table t value for a 0.95 probability level.< G    7  Hv GQHe+@ M ]`v <This is how the final answer should be reported, I.e. the mean the uncertainty. Note that units are given and the number of significant digits is to the same precision as the measured variable.< n^ Y #  S< D] `||   <\v +@jJY] `\v  0P<1To use Chauvenet's criterion to check for outliers, first calculate n, and sx. Then find t corresponding to a probability of 1 - 1/(2n) from the Appendix I table. Reject any observations that lie outside the range tsx. Do not apply Chauvenet's criterion a second time to the reduced data set.<P. 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