Question

I need help filling out the “Q-Test Determination” as well as the “Post-Lab Questions”

The directions are in the first three pictures, and the questions I need answered are in the last two pictures.

Thanks.

O-Test Datum Rejection We may be in a situation where one data value apparently has a strong influence on the mean of a set of data Assume we have 6 data points to analyze to be sure that each point is a viable part of the set: in other words, it's not "way off from the rest of the data. Consider the data set: 44.7 43.3 46.2 45.146.5 69.2 The 69.2 value appears to be out of class, i.c. it comes from a different population. Notice how this number affects the calculated mean: 44.7+43.3+46.2 +45.1+46.5+69.2 6 Whereas 44.7+ 43.3 +46.2 +45.1+46.5 45.16 Since the mean obtained using 69.2 is very different from the majority of the data, we suspect it is out of class. The O-test is often used to test this hypothesis. Like Student's t-test, we calculate a O value under a null hypothesis: i.e., data are the same, and then compare it to a statistical table value using the logical scheme Qable, then null hypothesis is correct f Qealculated Quable then null hypothesis is wrong f Qealculated In the latter event, we would reject the data. The O value is calculated using this formula: GAP Qcalc RANGE where the GAP is difference between the suspect datum (the one that looks out of place) and its nearest neighbor. The RANGE is the difference between the maximum and minimum data in the set. Rearranging the data set from minimum to maximum gives us: 43.3 44.7 45.1 46.2 46.5 69.2 Minimum valueMaximum value The RANGE and the GAP are RANGE = largest value minus smallest value = 69.2-43.3 = 25.9 GAPuspect datum minus its nearest neighbor = 69.2-46.5 22.7 and the calculatedO value is a0.876 calc 25.9 To determine if this value is acceptable, we look at the Table of @ Values for the number of measurement data (Table 1). Table 1: 0 Test Statistics (Rejection Quotients) 10 # of Data 0.56 0.51 0.47 0.44 0.41 Rejection Quotient 0.94 0.76 06 . 6 because we used data from 6 trials. Looking at Table 1, we see that In this case, N the Rejection Quotient (Cablel for 6 data values is 0.56. Because Qealculated (0.876) > Quble (0.56) we should reject the data value 69.2 from the set. Calculating the Mean (Average, Standard Deviation, and Relative Standard Deviation The mean or average result. . is calculated by summing the individual results and dividing this sum by the number (n) of individual values: The standard deviation is a measure of how precise the average is, that is, how well the individual numbers agree with each other. It is a measure of a type of error called random error the kind of error people can't control very well. It is calculated as follows: standard deviation, S The relative standard deviation (RSD) is often times more convenient. It is expressed in percent and is obtained by multiplying the standard deviation by 100 and dividing this product by the average. relative standard deviation, RSD-_ 100% × Example: Here are 4 measurements: 51.3,55.6,49.9 and 52.0. Calculate the mean, standard deviation, and relative standard deviation. 2088 =-=52.2 51.3+55.6 + 49.9 + 52 mean, X = 513-32211556-522+1499-522 (520-522 standard deviation, S 1/409+04 (23 02 .81- 1156+529 V5.9 = 2.4 relative standard deviation, RSD· x 1 o = 4.6% Our final result for this example can be written as 52.2 ± 2.4 or 52.2 ± 4.6%. Q-Test Data Sheet Sample Number 10 Mass of Pennies 1. 2975 3.070 3.068 3.110 3, IooA5 302 3.0 80 3,053 29, s3 2. Total mass of 10 pennies (added from above) 29, 547 3. Mass of 10 pennies (stacked together) 4. Mass of 10 pennies spread out on pan (measured together) Q-Test Determination 5. Value of suspect datum 6. Gap 7. Range 8. Q-Value Is it okay to reject this value? 9. 10. Show calculations for the Q-Test. Post-Lab Questions Determine the average, standard deviation, and relative standard deviation of your data (if you determined a data point should be rejected, then do not include it in your calculations). 1. 2. Given the accepted mass of a U.S. penny is 2.5 g. comment on the accuracy and precision of your data Provide an explanation for any discrepancy you find in lines 2 through 4 of your data sheet. 3.

Answer 1

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n te Qdable ,6, Value e do ta ゴ>noa, 7, e aver age can be obtuinec an 3-106 +3-070 +3.032 3.063 3-10 3-0 o S3 21.569 773.o 32 3-106 o o o 6 3. 07a o.ao o 2 9-082 -00D D oO6 3.068 O. 00 1 구 o.ooooo l4 3-o8อ 3-10 0 00033 3-02S2 3.053 ‘,00079 2o 020 49 2 O.2o49 3-812 0.645 % 3-02-2 ±0.665ソ. (2.4GR , 3.7462)

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