A student researcher developed a novel analytical method for determining the loa
ID: 3119158 • Letter: A
Question
A student researcher developed a novel analytical method for determining the load (Pb^2+) content in water. To demonstrate the efficacy of the new method, the researcher measured the Pb^2+ concentration an unknown sample using the novel method (Method 1). She then measured the same sample using the standard, conventional analytical method (Method 2). The results of this experiment are shown below as the mean (x) and standard deviation of the Pb^2+ concentration in ppm. The number of replicate measurements (n) is also shown. Method 1: x_1 = 3.370 ppm s_1 = 0.250 ppm n_1 = 6 Method 2: x_2 = 3.520 ppm s_2 = 0.200 ppm n_2 = 6 Calculate the F value. Are the standard deviations significantly different from each other at the 95% confidence level (Yes or No)? The value of F_table can be found in the table of critical F values. Calculate the value of t_calc to compare the data sets from Method 1 and Method 2. Can the student researcher assert that the new analytical method be considered a replacement for the conventional method with 99% confidence? A list of t values can be found in the Student's t table. Yes NoExplanation / Answer
a) F-value= S1^2/S2^2=
= .25^2/.2^2 = 1.5625
F_critical (5,5) = 5.05
since F<F_critical so, std dev are NOT significantly different.
(b) finding t value
t= (x1-x2)/SE
pooled std devi= Sp=SQRT((5*0.25^2+5*0.2^2)/(10))= .226
SE=std error = Sp*sqrt(1/6+1/6) = 0.131
t=-(3.37-3.52)/.131 = 1.145
(c) t_critical = 0.013
We reject the H0 (no diff bwteen 2 methods)
both methods are different.
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