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Chapter 4: Q19P (page 92)

If you measure a quantity four times and the standard deviation is 1.0% of the average, can you be 90% confident that the true value is within 1.2% of the measured average?

Short Answer

Expert verified

Yes, there is a 90% confidence level that the true value is within 1.2% of the measured average.

Step by step solution

01

Objective

The goal of this problem is to check whether the confidence interval for the true value is within 1.2% of the measured average at 90% confidence level.This means, tsn≈1.2%xor 0.012x

02

Determine the confidence Interval

Now, to solve, we will use the formula of the confidence interval (CI) :

CIforμ=x±2.3530.01x4=x±0.0118x≈0.012xis obtained from

Table 4 - 4 ; the degrees of freedom = 3 at 90 % confidence level.

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Most popular questions from this chapter

Here are mass spectrometric signals for methane inH2:

CH4(vol%):00.0620.1220.2450.4860.9711.921Signal(mV):9.147.595.6193.8387.5812.51671.9

(a) Subtract the blank value (9.1) from all other values. Then use the method of least squares to find the slope and intercept and their uncertainties. Construct a calibration curve.

(b) Replicate measurements of an unknown gave 152.1, 154.9, 153.9 and 155.1mV , and a blank gave 8.2,9.4,10.6 and 7.8mV . Subtract the average blank from the average unknown to find the average corrected signal for the unknown.

(c) Find the concentration of the unknown, its standard uncertainty (ux) , and the95%confidence interval.

What is the meaning of a confidence interval?

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

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.

(a) The linear calibration curve in Figure 4-13 isy=0.01630(±0.00022)x+0.0047(±0.0026)withsy=0.0059. Find the quantity of unknown protein that gives a measured absorbance of when a blank has an absorbance of 0.095

(b) Figure 4-13 has n=14 calibration points in the linear portion. You measure k=14replicate samples of unknown and find a mean corrected absorbance of 0.169 Find the standard uncertainty and 95%confidence interval for protein in the unknown.
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