Question

An environmental scientist developed a new analytical method for the determination of cadmium (cd^2+) in mussels. To validate the method, the researcher measured the Cd^2+ concentration in standard reference material (SRM) 2976 that is known to contain 0.82 plusminus 0.16 ppm Cd^2+. Five replicate measurements of the SRM were obtained using the new method, giving values of 0.782, 0.762, 0.825, 0.838, and 0.761 ppm Cd^2+. Calculate the mean (Bar x), standard deviation (s_x), and the 95% confidence interval for this data set. At list of t values can be found in the student's t table. X Bar = s_x = 95% confidence interval = x Bar plusminus Does the new method give a result that differs from the known result of the SRM at the 95% confidence level?

Answer 1

Answer:

The method is accurate  in the calculation of the $Cu^+2$

Explanation:

As a first step we have to calculate the average concentration of $Cu^+2$ find it by the method.

$\frac{0.782+0.762+0.825+0.838+0.761 }{5} =0.79 ppm$

Then we have to find the standard deviation:

$s=\sqrt{\frac{1}{N-1}\sum_{i=1}^N(x_i-\bar{x})^2}=0.0359$

For the confidence interval we have to use the formula:

μ=Average±$\frac{t*s}{\sqrt{n} }$

Where:

t=t student constant with 95 % of confidence and 5 data=2.78

μ= $0.79$  ±  $\frac{2.78*0.0359}{\sqrt{5} }$

upper limit:  0.84

lower limit: 0.75

If we compare the limits of the value obtanied by the method (Figure 1 Red line) with the reference material (Figure 1 blue line) we can see that the values obtained by the method are within the values suggested by the reference material. So, it's method is accurate.