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 = __—__ 45
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 44 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 44:
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 44: 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 44 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 ...
View
Full Document
 Summer '11
 Bonk

Click to edit the document details