General Chemistry I
General Chemistry I CHE 111
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This 2 page Class Notes was uploaded by Annamae Beatty on Wednesday September 30, 2015. The Class Notes belongs to CHE 111 at Pace University - New York taught by Staff in Fall. Since its upload, it has received 10 views. For similar materials see /class/217117/che-111-pace-university-new-york in Chemistry at Pace University - New York.
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Date Created: 09/30/15
Andrea Szczepanski Analytical Chemistry Fall 2001 Chapter 7 Statistical Analysis Evaluating the Data I Confidence Limits A Confidence limits define a numerical interval around x7 experimental mean that contains u the mean for a population with a certain probability B Confidence interval is the numerical magnitude of the confidence limit It is computed from the standard deviation and depends on how accurately we know s the sample standard deviation compared to o the population standard deviation In the absence of bias and assuming s the sample standard deviation is a good estimate of o the population standard deviation The confidence limit CL for a single measurement can be expressed by CL xi 20 The confidence limit for N measurements can be expressed by CL x7 i Q N square root In determining the confidence levels expressed as a percent we can examine the normal bell curve INSERT 5 Bell CURVES from PAGE 150 HERE and EXPLAIN Example 75 page 173 a 90 Confidence Limit 853 ug CumL i 164 X 032 ug CumL square root ofl 853 1053ug CumL 99 Confidence Limit 853 ug CumL i 258 X 032 ug CumL square root of 1 853 080ug CumL b 90 Confidence Limit 853 ug CumL i 164 X 032 ug CumL square root of 4 853 1026ug CumL 99 Confidence Limit 853 ug CumL i 258 X 032 ug CumL square root of 4 853 1040ug CumL c 90 Confidence Limit 853 ug CumL i 164 X 032 ug CumL square root of 16 853 0l3ug CumL 99 Confidence Limit 853 ug CumL i 258 X 032 ug CumL square root of 16 853 02lug CumL Andrea Szczepanski Analytical Chemistry Fall 2001 These concepts also apply when 0 is not known and we are dealing with a very small sample H Hypothesis Testing A The null hypothesis INSERT FURTEHR EXPLANATION 1 Comparisons of Experimental Mean a Comparing Experimental Mean with True Value HI Detecting Gross Errors A Outliers 7 data points that differ excessively from the mean in a data set B Retention or Rejection of Outliers 1 Q Test 7 the absolute value of the difference between the questionable result and its nearest value is divided by the spread of the entire set Qex 3 A P 9 W Q exp is then compared with rejection values Q m INSERT TABLE 73 page 158 Example 7l7 page 174 a Q exp 85107 8470 083 Q cm 0970 85107 8462 Q up ltQ cm RETAIN b b Q m 85107 8470 083 Q m 0829 85107 8462 Q up gt Q crit REJECT C Dealing with outliers in small sets of data 1 Reexamine all data relating to the outlying results to see if gross error could have affected its value This demands a properly kept lab notebook containing careful notations of all observations 2 If possible estimate the precision that can be reasonable expected from the procedure to be sure that the outlying result is actually questionable Repeat the analysis if sufficient sample and time are available If more data cannot be obtained apply the Q test to the existing set of data to see if the doubtful result should be retained or rejected on statistical ground 5 If the Q test indicates retention consider reporting the median of the set rather than the mean The median has the greater virtue of allowing inclusion of all data in a set without undue in uence from an outlying value In addition the median of a normally distributed set containing three measurements provides a better estimate of the correct value than the mean of the set after the outlying value has been discarded 5