Confidence line

We selected three stars with [Fe/H] < — 3, which were known to have [Ba/Fe] — 1, typical for their metallicities, and estimate Eu abundance using Subaru HDS. As shown in Fig. 1, our data add the lowest detections of Eu, at [Fe/H] < —3. The three stars and most others are located between the 50% confidence lines for this case. However, if Eu comes from more massive stars, these stars are located outside the 90% confidence region. We suggest, therefore, the r-process site is most likely to be SNe from low-mass progenitors such as 8 — 10M0 stars. 

The 95% confidence lines are drawn around the best-fit regression ploS of peak response vs. analyte concentration. A horizontal line is drawiD from the y-intercept of the upper 95% Cl line to the lower 95% Cl line. vertical line is drawn from the intersection point on the lower 95% Cg line to the x-axis, yielding the x-intercept. The x-intercept is the LODg whereas the LOQ is 3.3LOD (Fig. 5). ... 

Figure 10.16. Schematic E sort, (a) A regression line used as the predictor for four categories (1) accepted correctly (2) accepted incorrectly (3) rejected correctly and (4) rejected correctly, (h) With the lower confidence line used as the predictor, then a relatively low proportion of material lies in the accepted incorrectly category (lower right).

The limit of determination indirectly relates to the limit of detection. It is the concentration level from where a determination can be performed with a preset precision. The definition can be understood from the confidence lines at each side of the calibration curves (Fig. 15), which diverge both at lower concentrations, as a result of sample inhomogeneities or noise magnitude, as well as at large concentrations, as a result of deviations from linearity in the calibration or source instabilities. 

Three types of tests are discussed. The first two tests require graphs of the number of blacks vs. the sequence number of samples (the mixture consists of black and natural polythene colored particles). One test looks for the number of samples outside of certain control limits or confidence lines and the other looks for the number of consecutive samples on one side of the mean. The third test requires computing b = s2/x, where... 

FIGURE 2.25. Koutecky-Levich analysis of the first unmediated oxidation wave in Fig. 2.24. The linear regression line and the 98% confidence lines are also illustrated. 

The complete (shown in the following inclusive of weighting) equations can be found in Ref. [8] or papers cited therein. Here, the two square roots should be replaced by a factor of 1.2, which leads (without weighting) to the approximation of two constant confidence lines parallel to the straight line. Visualized, these confidence lines would be elastically fixed at the ends and slightly pressed in the middle. This is exactly the effect of the real square-root term, for which using ordinary linear regression (iv ) must be set to 1 and Ziv = n. 

Using the ternary tie-line data and the binary VLE data for the miscible binary pairs, the optimum binary parameters are obtained for each ternary of the type 1-2-i for i = 3. .. m. This results in multiple sets of the parameters for the 1-2 binary, since this binary occurs in each of the ternaries containing two liquid phases. To determine a single set of parameters to represent the 1-2 binary system, the values obtained from initial data reduction of each of the ternary systems are plotted with their approximate confidence ellipses. We choose a single optimum set from the intersection of the confidence ellipses. Finally, with the parameters for the 1-2 binary set at their optimum value, the parameters are adjusted for the remaining miscible binary in each ternary, i.e. the parameters for the 2-i binary system in each ternary of the type 1-2-i for i = 3. .. m. This adjustment is made, again, using the ternary tie-line data and binary VLE data. 

The optimum parameters for furfural-benzene are chosen in the region of the overlapping 39% confidence ellipses. The ternary tie-line data were then refit with the optimum furfural-benzene parameters final values of binary parameters were thus obtained for benzene-cyclohexane and for benzene-2,2,4-trimethyl-pentane. Table 4 gives all optimum binary parameters for this quarternary system. 

If the parameters were to become increasingly correlated, the confidence ellipses would approach a 45 line and it would become impossible to determine a unique set of parameters. As discussed by Fabrics and Renon (1975), strong correlation is common for nearly ideal solutions whenever the two adjustable parameters represent energy differences. 

Fig. X-7. Advancing and receding contact angles of octane on mica coated with a fluo-ropolymer FC 722 (3M) versus the duration of the solid-liquid contact. The solid lines represent the initial advancing and infinite time advancing and receding contact lines and the dashed lines are 95% confidence limits. (From Ref. 75.)...

Example 14 For the best-fit line found in Example 13, express the result in terms of confidence intervals for the slope and intercept. We will choose 95% for the confidence interval. 

Three replicate determinations are made of the signal for a sample containing an unknown concentration of analyte, yielding values of 29.32, 29.16, and 29.51. Using the regression line from Examples 5.10 and 5.11, determine the analyte s concentration, Ca, and its 95% confidence interval. 

Management and Employee Cooperation. Before beginning to collect data, the cooperation of the managers involved, including the first line supervisor, and of the workers should be secured. Management needs to be informed so that they can be confident that surveillance activities will not upset production or lead to injuries. Workers need to know what the valuation means to them and how the results are to be reported. Everyone needs to know how the measurement is to be conducted so that the actual measurement causes as Htde dismption as possible. 

Cost to the Industry. When compared to the potential expense for defending a single claim of tampering, the cost of effective tamper-evident packaging becomes insignificant. Many firms simply caimot afford the cost of responding to product tampering claims, especially if the firm is a small one with a limited or totally related product line where the reputation of the entire product line can be affected by adverse pubHcity on one item. LiabiUty insurance caimot return lost customer confidence. 

Fig. 9. The two materials, A and B, have overlapping 95% confidence limits at the LD q level. Because the slopes of the dose—mortahty regression lines for both materials are similar, there is no statistically significant difference in mortahty at the LD q and LD q levels. Both materials may be assumed to be lethahy equitoxic over a wide range of doses, under the specific conditions of the test.

Fig. 12. The relationship between the mean oceanic residence time, T, yr, and the seawater—cmstal rock partition ratio,, of the elements adapted from Ref. 29. , Pretransition metals I, transition metals , B-metals , nonmetals. Open symbols indicate T-values estimated from sedimentation rates. The sohd line indicates the linear regression fit, and the dashed curves show the Working-Hotelling confidence band at the 0.1% significance level. The horizontal broken line indicates the time required for one stirring revolution of the ocean, T. ...

Fig. 13. The standard addition method where MB is the confidence interval for the slope of the line = k, and represents 95% confidence interval (14).

The presence of errors within the underlying database fudher degrades the accuracy and precision of the parameter e.stimate. If the database contains bias, this will translate into bias in the parameter estimates. In the flash example referenced above, including reasonable database uncertainty in the phase equilibria increases me 95 percent confidence interval to 14. As the database uncertainty increases, the uncertainty in the resultant parameter estimate increases as shown by the trend line represented in Fig. 30-24. Failure to account for the database uncertainty results in poor extrapolations to other operating conditions. 

The key phrase in this clause is or otherwise verified as it allows you to receive product into your company and straight onto the production line if you have verified that it conforms to the specified requirements before it arrives. An example of this is where you have performed acceptance tests or witnessed tests on the supplier s premises. You may also have obtained sufficient confidence in your supplier that you can operate a Just-in-time arrangement but you must be able to show that you have a continuous monitoring program which informs you of the supplier s performance. 

Sampling inspection should be used when statistical data is unavailable to you or you don t have the confidence for permitting ship to line. 

For example, a facility manager may be confident that PSM policies and procedures are in place, but line personnel may indicate in the same survey that they are unaware of them—suggesting a gap that your implementation plan should address. 

Calculations of the confidence intervals about the least-squares regression line, using Eq. (2-100), reveal that the confidence limits are curved, the interval being smallest at Xj = x. 

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