National banking under the Federal Reserve System

Grundriß des deutschen Zollrechts

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Monograph

Identifikator:: 1757542345

URN:: urn:nbn:de:zbw-retromon-135097

Document type:: Monograph

Title:: National banking under the Federal Reserve System

Place of publication:: New York

Publisher:: The National City Bank of New York

Year of publication:: 1927

Scope:: 154 S.

Digitisation:: 2021

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: Federal reserve act (approved Dec.23,1913)

Collection:: Economics Books

2 - THEORY OF STATISTICS. It will be observed that if n, be very small compared with ny €,; approaches, as it should, the standard error for a sample of n, observations. We omit, in this case, the allied problem whether, if the difference between p, and p, indicated by the samples were real, it might be wiped out in other samples of the same size by fluctuations of simple sampling alone. The solution is a little complex as we no longer have &=p.q,/(n; + ny). Example v.—Taking the data of Example iii., suppose that we compare the proportion of tall plants amongst the offspring resulting from cross-fertilisations (viz. 50 per cent.) with the proportion amongst all offspring (viz. 29/68, or 42:6 per cent.). As, in this case, both the subsamples have the same number of observations, n, =n,= 34, and 20 39 IN n= 00x 1) ~ 0-060 or 6 per cent. Asin the working of Example iii., the observed dif- ference is only 1°25 times the standard error of the difference, and consequently it may have arisen as a mere fluctuation of sampling. Example vi.—Taking now the figures of Example iv., suppose that we had compared the proportion of girls of medium hair- colour in Edinburgh with the proportion in Glasgow and Edinburgh together. The former is 41'1 per cent. the latter 435 per cent., difference 24 per cent. The standard error of the difference between the percentages observed in the sub- sample of 9743 observations and the entire sample of 49,507 observations is therefore Bin, nN 39,764 Y= ; ep = (43'5 x 56:5) (ress — 0°45 per cent. The actual difference is over five times this (the ratio must, of course, be the same as in Example iv.), and could not have occurred as a mere error of sampling. REFERENCES: The theory of sampling, for the cases dealt with in this chapter, is generally treated by first determining the frequency-distribution of the number of successes in a sample. This frequency-distribution is not considered till Chapter XV., and the student will be unable to follow much of the literature until he has read that chapter. Experimental results of dice throwing, coin tossing, etc. (1) QUETELET, A., Leltres . . . . sur la théorie des probabilités ; Bruxelles, 1846 (English translation by O. G. Downes; C. & E. Layton, London, 1849). See especially letter xiv. and the table on p. 374 of the French, p. 255 of the English, edition. 7

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