T-values table

Ot = significance level, usually set at. 10,. 05, or. 01 t = tabled t value corresponding to the significance level Ot. For a two-tailed test, each corresponding tail would have an area of Ot/2, and for a one-tailed test, one tail area would be equal to Ot. If O" is known, then z would be used rather than the t. t = (x- il )/ s/Vn) = sample value of the test statistic. 

Step 2 Let us set a = 0.05. Because this is a two-tail test, the t tabled ( t) value uses ajl from Table B. 

The decision rule, Step 4, is based on the significance level (") of 0.05. If the f-test performed calculates a t value of less than the tabled t value at " = 0.05, then the null hypothesis, no detectable difference between samples, will be accepted. If the f-test performed calculates a t value greater than the tabled t value at" = 0.05, then the null hypothesis will be rejected—there is a significant difference between samples. 

Table t Values Fit for Molality Mean Ionic Activity Coefficient Data of Aqueous Electrolytes at 298,15 K... 

The characteristic isotherm concept was elaborated by de Boer and coworkers [90]. By accepting a reference from a BET fit to a standard system and assuming a density for the adsorbed film, one may convert n/rim to film thickness t. The characteristic isotherm for a given adsorbate may then be plotted as t versus P/P. For any new system, one reads t from the standard r-curve and n from the new isotherm, for various P/P values. De Boer and co-work-ers t values are given in Table XVII-4. A plot of t versus n should be linear if the experimental isotherm has the same shape as the reference characteristic isotherm, and the slope gives E ... 

The t-values in this table are for a two-tailed test. For a one-tailed test, the a values for each column are half of the stated value, column for a one-tailed test is for the 95% confidence level, a = 0.05. For example, the first... 

From standard Student tables, the value for t l/fT= 1.049 at the 95% confidence level. Thus, mean value = 56.3 13.0 (95% confidence level) and one could be confident that 95% of measured values would fall in the range 69.3 - 43.3. This is a large range and is not very precise. 

By combining Eqs. (8.42), (8.49), and (8.60), show that Vi°(52 - 5i) = (l/2)RTj., where T. is the critical temperature for phase separation. For polystyrene with M = 3 X 10, Shultz and Floryf observed T. values of 68 and 84°C, respectively, for cyclohexanone and cyclohexanol. Values of Vi° for these solvents are abut 108 and 106 cm mol", respectively, and 5i values are listed in Table 8.2. Use each of these T. values to form separate estimates of 62 for polystyrene and compare the calculated values with each other and with the value for 62 from Table 8.2. Briefly comment on the agreement or lack thereof for the calculated and accepted 5 s in terms of the assumptions inherent in this method. Criticize or defend the following proposition for systems where use of the above relationship is justified Polymer will be miscible in all proportions in low molecular weight solvents from which they differ in 5 value by about 3 or less. 

Table 5. Values of the Diffusion Coefficient and of M-c/T Apc Various Gases in Air at 0°C and at Atmospheric Pressure ...

The aimual production of pet foods is approximately 6.35 x 10 t, valued at 7.6 biUion (Table 2). It has been estimated that there are as many as 15,000 different brand labels and package sizes of pet foods, marketed by 3000 manufacturers (30). Conservative estimates are closer to 3000 brands (31) and sizes, with 1800—1900 registered iu the state of Texas. 

Direct dyes are one of the most versatile classes of dyestuff. U.S. production in 1988 was nearly 18,900 t valued at 100 million. In worldwide usage for ceUulosic textiles, direct dyes are the second largest class of dyestuff. The AATCC Buyers Guide (July 1991) Usts over 180 different Cl categories for direct dyes representing nearly 850 commercially available products. U.S. production figures are not released for most of these dyes the important direct yeUows and oranges of revealed chemical composition are Usted in Table 5. 

You can t duplicate these molecular weights for C7H16 and CsHa02 by using the atomic weights given in the periodic table. Those values are for the natural-abundance mixture of isotopes. The exact values are 12.00000 for C, 1.00783 for H, and 15.9949 for 0. 

The MP2 and CCSD(T) values in Tables 11.2 and 11.3 are for correlation of the valence electrons only, i.e. the frozen core approximation. In order to asses the effect of core-electron correlation, the basis set needs to be augmented with tight polarization functions. The corresponding MP2 results are shown in Table 11.4, where the A values refer to the change relative to the valence only MP2 with the same basis set. Essentially identical changes are found at the CCSD(T) level. 

The formula for minimum plastic collapse pressure is applicable for D/t values as shown in Table 4-151. The factors A, B, and C are given in Table 4-152. 

From the t-tables, the value of t for the 95 per cent confidence level with (n— 1), i.e. three degrees of freedom, is 3.18. 

It is then related to a set of t-tables (Appendix 12) in which the probability (P) of the t-value falling within certain limits is expressed, either as a percentage or as a function of unity, relative to the number of degrees of freedom. 

Once equation (10.158) has been obtained for relating Cy. m to T for a Debye solid, equations relating (Um - U0 m), (Hm - Uo.m), and Sm to T can be derived. Tables of values, expressed in terms of 9d/T. can be found in Table A4.7, Appendix 4, with more extensive tables found in the literature1 to calculate these thermodynamic properties. 

This would not be expected simply on the basis of a crystal-field model, for the d orbitals will contract with increasing positive charge and hence interact less well with the ligand point charges . The modest decreases in bond length as one traverses the series (Eq. 6.9) are unlikely to compensate for, let alone override, the effects of such orbital contraction. Finally, to add to the confusion, we also note from Eq. (6.7) that zio -t values increase as we go down the periodic table (Eq. 6.10). 

In this equation, r) the absolute hardness, is one-half the difference between /, the ionization potential, and A, the electron affinity. The softness, a, is the reciprocal of T]. Values of t) for some molecules and ions are given in Table 8.4. Note that the proton, which is involved in all Brdnsted acid-base reactions, is the hardest acid listed, with t — c (it has no ionization potential). The above equation cannot be applied to anions, because electron affinities cannot be measured for them. Instead, the assumption is made that t) for an anion X is the same as that for the radical Other methods are also needed to apply the treatment to polyatomic... 

Example 61 The raw data, given as %-of-nominal values with one decimal place, are found in Table 4.37 For each group of 10 values the mean and the standard deviation were calculated. Using these, the t-values for the differences L - mean, with L = 75, 85, 115, resp. 125% were determined they are all above 2.9, indicating low risk. The corresponding CP-values were calculated the differences ACP75-85 and ACP 15-125 were added and multiplied by 100 to obtain the approximate risk, in %, of finding a result between the inner and the outer limits. For a content uniformity test with n = 10 tablets, a risk of 0.003872% translates into a deviant result once every 20-25 trials, or, with six CU runs per batch, every third or fourth batch. 

Slope expressed as the contribution from each R radical. If the AE(t) values of Table I are used, the overall magnitude of the slope would be 9.76 for reaction 1 at one hour half life, for example. 

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