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Ttest2

# Ttest2 - Chemically generated Nitrogen from nitrolgen air...

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Unformatted text preview: Chemically generated Nitrogen from _ nitrolgen air 00300 00 I (SEED I l I r L_l l I _I_ I I l I i I _I. l I l_L I l 2.295 2.300 2.305 2.310 2.315 Mass (9) Let’s see how to use the t test to decide whether nitrogen isolated from air is “signiﬁcantly” heavier than nitrogen isolated from chemical sources. For two sets of data consisting of n; and n2 measurements (with averages in and E2), we calcu- late a value of it from the formula t Test for comparison I = l_J_Ci_—3'E_2l ”I”: (4 4) of means: spwled n1 -l- n; 2 2 (51011 — 1) + 32012 — 1) where s = __—__ 4-5 P00de 71] + 712 _ 2 { ) Here spooicd is a pooled standard deviation making use of both sets of data. The absoiute value of i1 — E2 is used in Equation 44 so that t is always positive. The value of r from Equation 4-4 is to be compared with the value of r in Table 4—2 for (H1 + n2 — 2) degrees of freedom. if the calculated 1‘ is greater than the tabulated t at the 95% conﬁdence levei, the two resaits are considered to be dtﬁferenr. Is Rayleigh's N; from Air Denser than N2 from Chemicals? The average mass of nitrogen from air in Table 4.3 is E1 = 2.310 109 g, with a stan- dard deviation of \$1 = 0.000 143 (for n1 = 7 measurements). The average mass from chemical sources is E; = 2.299 472 g, with a standard deviation of s; = 0.001 379 (for n2 = 8 measurements). Are the two masses signiﬁcantly different? SOLUTION To answer this question, we calculate spooked with Equation 4—5, 0.000 1432 7 — 1 + 0.001 37 3 8 — 1 _ spaciarJ ( 7+)s—2 °( )—0.001017 and t with Equation 4-4: t - 2.310 109 — 2.299 475 7 - s _ 202 0.001 017 7 + 8 For "i + 8 — 2 = 13 degrees of freedom in Table 4—2, tlies between 2.228 and 2.131 at the 95% conﬁdence level. The observed value (t = 20.2) is greater than the tab- ulated it, so the difference is signiﬁcant. In fact, the tabulated value of I for 99.9% conﬁdence is about 4.3. The difference is significant beyond the 99.9% conﬁdence level. Our eyes do not lie to us in Figure 4-4: N2 from the air is undoubtedly denser than N2 from chemical sources. This observation led Rayleigh to discover argon as a heavy constituent of air. FIGURE 4-4 Lord Rayleigh’s measurements of the mass of nitrogen isolated from air or generated by decomposition of nitrogen compounds. Rayleigh recognized that the difference between the two data sets was outside of experimental error. He deduced that a heavier com- ponent, which turned out to be argon, was present in nitrogen isolated from air. If Icaiculated ) Enable (95%): the differ— ence is signiﬁcant, Statistical tests only give us proba— bilities.'Thcy do not relieve us of the ultimate subjective decision to accept or reject a conclusion. 61 ...
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