Percentage Points, --Distribution

Suppose, for example, that an estimate based on a Wei-bull fit to the fan data is desired of the fifth percentile of the distribution of time to fan failure. Enter the Weibull plot. Figure 62.6, on the probability scale at the chosen percentage point, 5 per cent. Go vertically down to the fitted line and then horizontally to the time scale where the estimate of the percentile is read and is 14,000 hours. 

The table gives the value of f . — the 100a percentage point of the t-distribution for v degrees of freedom. 

APPENDIX 11 CHARACTERISTIC INFRARED ABSORPTION BANDS 839 APPENDIX 12 PERCENTAGE POINTS OF THE f-DISTRIBUTION 840 APPENDIX 13 / -DISTRIBUTION 841 APPENDIX 14 CRITICAL VALUES OF 0 (/> = 0.05) 842 APPENDIX 15 CRITICAL VALUES OF THE CORRELATION COEFFICIENT p (P = 0.05) 842... 

The 100(1 — a)% confidence interval for fi is given by (Jr Ka/2percentage point of the normal distribution. This result is obtained by considering the distribution of [(x — /u,) /N/a], which is normally distributed with mean 0 and standard deviation 1. Hence,... 

From the tables [Percentage Points of the /-Distribution] the value of t for (n freedom at 95% confidence level is 2.09. 

A particular use of the t-statistic is calculating confidence intervals (Cl). When we calculate the mean of a sample we do not expect that it will be exactly equal to the mean of the population from which the sample was drawn. Nonetheless, we can expect that it will be reasonably close to the population mean. A confidence interval provides an estimate as to how close. The 95% confidence interval is a random interval such that, in 95% of hypothetical replications of the sampling process, the confidence intervals obtained will include the true value of p The confidence interval for p is of the form x multiples of s.e.m. The multiple used is tl-a/2 (n-1), which is the 100(l-o/2) percentage point of the t-distribution with n-1 degrees of freedom. Thus, the 95% Cl (o=0.05) is given by ... 

Here F(p, n — p, 1 — a) is the a percentage point of the Fischer s F distribution at p and ( - p) degrees of freedom. The boundary of the joint confidence region is defined by all values of P which satisfy the hyperellipsoid in the / -dimensional parameter space around b,... 

Tables B1-B3 have been taken from M. Merrington and CM. Thompson, Tables of percentage points of the inverted beta (F) distribution, Biometrika 33 (1943) 73.

Table G-3 compares costs of production, distribution, and administration as a percent of sales in each year following market approval under the two methods of cost estimation. The marginal cost estimate, which represents an upper bound on actual costs, is higher than the financial statement estimates in most years. It is much higher (by up to 13 percentage points) in the early years. The marginal cost estimate includes both marketing costs for generic companies, which may be as much as 6 percent of sales, and an implicit rental cost of facilities and equipment, while the financial statement estimates given in the table do not include these costs. It also includes the cost of ongoing R D for generic companies, which comprise approximately...

The experiments of the second kind, that is, without simulation of the initial water saturation, were carried out at temperature of 200°C. Results recorded in Table 8 for experiment No. 7 show that, in this case, the displacement coefficient amounted to 78.3%. This value was 5.3 percentage points lower than results obtained in experiment No. 6, that is, with the simulation of water saturation. The displacement of liquids from the bed is more complete in instances when initial water saturation is simulated. This phenomenon is explained by the character of distribution of oil and water in the bed and by the surface properties of die porous medium. 

At low temperatures, the calculated pentad distributions for 1 and 2 are in excellent agreement with experiment, with overall RMS deviations at 10 °C amounting to 1.6 and 1.2 percentage points, respectively. The theoretical pentad distribution for 1 reflects slightly less syndiospecificity than found in analysis of the NMR spectrum, whereas 2 along with the related, sterically more encumbered catalyst 8, is predicted to be somewhat too isospecific. The... 

For 3, the predicted pentad distribution is inaccurate (RMS deviations above 5 percentage points) even at low temperatures. This catalyst is normally referred to as hemiisospecific, although the low intensities observed for the rrrr pentad suggest that weakly isospecific perhaps is a better term. With one olefin coordination site being ideally enantio-... 

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