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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

Traces of toxic, man-made hexachlorohexanes in North Sea sediments were extracted by a known process and by two new procedures, and measured by chromatography.

(a) Is the concentration parts per million, parts per billion, or something else?

(b) Is the standard deviation for procedure B significantly different from that of the conventional procedure?

(c) Is the mean concentration found by procedure B significantly different from that of the conventional procedure?

(d) Answer the same two questions as parts (b) and (c) to compare procedure A to the conventional procedure.

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

A Standard Reference Material is certified to contain 94.6 ppm of an organic contaminant in soil. Your analysis gives values of 98.6,98.4,97.2,94.6, and 96.2ppm. Do your results differ from the expected result at the 95% confidence level? If you made one more measurement and found 94.5, would your conclusion change?

For the numbers 116.0,97.9,114.2,106.8and 108.3, find the mean, standard deviation, standard uncertainty ( = standard deviation of the mean), range, and 90% confidence interval for the mean. Using the Grubbs test, decide whether the number 97.9should be discarded.

What fraction of vertical bars in Figure 4-5a is expected to include the population mean (10000) if many experiments are carried out? Why are the 90 % confidence interval bars longer than the 50 % bars in Figure 4-5?
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