Case example of Statistical Analysis:



A Case example of Statistical AnalysisAn investigator at a university ordered a compound from a chemical house and wanted to verify the purity. The substance is known to be optically active, has the property that it will rotate the orientation of plane polarized light by an amount that is directly proportional to its concentration. The formula for specific rotation is given as:αs= VL?m?αwhere V is the volume of the solution in, L is the length of the polarimeter tube, m is the mass of the solute and is the measured rotation from the polarimeter.The investigator instructed a research student to measure the rotation of a sample of the standard compound and calculate the specific rotation. The student reported preparing a solution by measuring 1.5220 g of the dry substance, dissolving it in water and diluting to 25.00 ml in a volumetric flask. A sample was placed in a standard polarimeter tube of length 2.000 dm. The student then adjusted the thermostat bath such that it would hold a temperature between 24.8oC and 25.3oC. Obtained, was the following data: (deg)20.04 20.07 20.05 20.09 20.04 20.02 20.04 20.03 20.06 20.05 The student estimated the error in the measured values as:V = 0.02 ml, mass = .0003 gm, and L = 0.002 dm.The student then examined the data and determined that the value, 20.09 was an outlier and discarded the data point. (See Rejection of Data below)Following the discarding of the selected data point, calculate the average and standard deviation for this set of measurements using the student-t tables at 95% confidence. Average = _______________ Standard Deviation = ______________ Student-t value from table = _____________Reported average with error: ________________ +/- ____________ ________unitsCalculate the specific rotation and the expected error in the specific rotation by carrying out a differential error analysis. Include units and report your answer and the associated error in units of deg-cm3/gm-dm. s = ____________________ +/- ____________ deg-cm3/gm-dmWhich measurement contributed most to the expected error? __________________The literature value of specific value for this substance is known to be +152.70 deg-cm3/gm-dm. The data as determined, as you should find, did not agree with literature, so the investigator began looking for sources of error in the students work.Evaluate the student’s decision to discard the data point. Carry out a Q-test and determine whether the student was correct in discarding the data point. If the data point cannot be discarded, recalculate the specific rotation.Based on your answer in 4.), is it necessary to recalculate the error in the specific rotation? Explain.You should find that the data with its standard deviation still does not encompass literature. Under further investigation, it was found that the balance used to weigh the compound had a digital output that had a burned out LED. It was possible that the “5” in the weight is really a “6”. Recalculate the specific rotation and error. Determine if the data is closer to literature. s = ____________________ +/- ____________ deg-cm3/gm-dmWhat kind of error is this? _______________________Upon further investigation of the experimental setup, it was found that the heating element was never turned on and, thus, the temperature under which the measurements were made was really 18.0oC, rather than the desired 25.0oC. The correction for temperature can be made as follows:The densities of this solution at the two temperatures are roughly the same as that of water since the solutions are so dilute. The densities of water at these two temperatures are:Density(25oC) = 0.998625 gm/mlDensity(18oC) = 0.997075 gm/mlMake the correction for temperature and recalculate the value for the specific rotation.s = ____________________ +/- ____________ deg-cm3/gm-dmWhat type of error is this? _____________________The number calculated is surely coming closer to the literature result, but you should find that it is still off. The investigator, being a bit confounded for this reason examined the student laboratory notebook. He noticed that a blank was never used to calibrate the polarimeter. Investigating this, a polarimeter tube was filled with deionized water and placed the in the polarimeter. The resulting measurement was found to be 0.22, rather than the correct value of 0.0. What type of error is this? _____________________Correct the average measured rotation by subtracting the reference value. Recalculate the specific rotation. Verify that the average value +/- the standard deviation now agrees with literature indicating a substance of appropriate purity.s = ____________________ +/- ____________ deg-cm3/gm-dm ................
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