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Chapter 4: QFE (page 90)

A reliable assay shows that the ATP (adenosine triphosphate) content of a certain cell type is. You developed a new assay, which gave the values117,119,111, 115, 120渭mol/100mL(average = 116.4) for replicate analyses. Do your results agree with the known value at the 95%confidence level?

Short Answer

Expert verified

The 95% confidence interval does not include the accepted value of111渭mol/100mL

Step by step solution

01

Definition of standard deviation and mean.

  • Arithmetic mean: By dividing the amount of measured values by the number of measurements , the arithmetic mean x炉is determined.

Mean:

  • Standard deviation: The standard deviation is a measurement of how tightly the data cluster around the mean.

The standard deviation (s) is given by the formula:

s=鈭�ixi-x炉2n-1

Standard deviation of the mean of sets of n values is:

蟽n=胃n

02

Explanation.

The mean:

x炉=鈭�ixin=117+119+111+115+1205=116.4=116roundedoff

Standard deviation:

s=鈭�xi-x炉2n-1=116-1172+.....+116-12025-1=3.58=4roundedoff

95% Confidence interval:

The 95% confidence interval for four degrees of freedom is calculated as follows,

Confidence interval=x炉卤tsn

=116.4卤2.7763.585=116.4卤4.4=116卤4roundedoff=112.0

or 120.8 (digits in subscript denotes insignificant figures)

The 95% confidence interval does not include the accepted value of111渭mol/100mL Hence, the difference is significant.

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Most popular questions from this chapter

What is the relation between the standard deviation and the precision of a procedure? What is the relation between standard deviation and accuracy?

Logarithmic calibration curve. Calibration data spanning five orders of magnitude for an electrochemical determination of p-nitrophenol are given in the table. (The blank has already been subtracted from the measured current.) If you try to plot these dataon a linear graph extending from 0 to 310渭驳/mLand from 0 to 5260nA, most of the points will be bunched up near the origin. To handle data with such a large range, a logarithmic plot is helpful.

Overwhatrangeisthelog-logcalibrationlinear?

(a) Make a graph of log (current) versus log( concentration). Over what range is the log-log calibration linear?

(b)FindtheequationoftheLine

InTheform log(current)=m脳log(concentration)+b

(c) Find the concentration of p-nitrophenol corresponding to a signal of 99.9nA.

(d) Propagation of uncertainty with logarithm. For a signal of 99.9nA, log (concentration) and its standard uncertainty turn out to be 0.68315卤0.04522. With rules for propagation of uncertainty from Chapter 3, find the uncertainty in concentration.

Here is a least-squares problem that you can do by hand with a calculator. Find the slope and intercept and their standard deviations for the straight line drawn through the points(x,y)=(0,1),(2,2)and (3,3). Make a graph showing the three points and the line. Place error bars (卤sy)on the points.

Suppose that you carry out an analytical procedure to generate a linear calibration curve like that shown in Figure 4-13. Then you analyse an unknown and find an absorbance that gives a negative concentration for the analyte. What might this mean?

Should the value 216 be rejected from the set of results 192,216,202,195, and 204?
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