An Introduction to the theory of statistics

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Monograph

Identifikator:: 1751730271

URN:: urn:nbn:de:zbw-retromon-127610

Document type:: Monograph

Author:: Yule, George Udny http://d-nb.info/gnd/12910504X

Title:: An Introduction to the theory of statistics

Edition:: 8. ed. rev

Place of publication:: London

Publisher:: Griffin

Year of publication:: 1927

Scope:: XV, 422 S; Ill., Diagr

Digitisation:: 2021

Collection:: Economics Books

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Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Part III. Theory of sampling

Collection:: Economics Books

XIIL.—SIMPLE SAMPLING OF ATTRIBUTES, 275 4. The proportion of successes in the data of Qu. 1is 0°5097. Find the stand- ard-deviation of the proportion with the given number of throws, and state whether you would regard the excess of successes as probably significant of bias in the dice. 5. In the 4096 drawings on which Qu. 2 is based 2030 balls were black and 2066 white. Is this divergence probably significant of bias? 6. If a frequency-distribution such as those of Questions 1, 2, and 3 be given, show how =» and p, if unknown, may be approximately determined from the mean and standard-deviation of the distribution. Find 2 and p in this way from the data of Qu. 1 and Qu. 3. 7. Verify the following results for Table VI. of Chapter IX. p. 163, and compare the results of the different grouping of the table on p. 263. In calculating the actual standard-deviation, use Sheppard’s correction for grouping (p. 212). Actual Standard- Row or Rows. Mean, Standard- deviation * deviation s. of Sampling s,. 5082 1160 11°18 5095 6:79 6°45 510°0 528 5-00 4 5111 5:03 422 G 5102 367 373 6, 7 5097 4°13 3°24 8,9,10,'11 5087 3°10 2°69 12, 13, 14 5084 255 2:25 15 and upwards. 508-2 2°13 1-85 8. In a case of mice-breeding (see reference given in § 11) the harmonic mean number in a litter was 4735, and the expected proportion of albinos 50 per cent. Find the standard-deviation of simple sampling for the pro- portion of albinos in a litter, and state whether the actual standard-deviation (21°63 per cent. ) probably indicates any real variation, or not. 9. (Data from Report i., Evolution Committee of the Royal Society, p. 17.) In breeding certain stocks 408 hairy and 126 glabrous plants were obtained. If the expectation is one-fourth glabrous, is the divergence significant, or might it have occurred as a fluctuation of sampling ? 10. (Data of Example ix. and Qu. 5, Chap. IIL.) Is the association in either of the following cases likely to have arisen as a fluctuation of simple sampling ? (a) (4B)=47 (48)=12 (eB)=21 (aB)=3 (®) (4.B)=309 (48)=214 (aB)=132 (aB)=119 11. The sex-ratio at birth is sometimes given by the ratio of male to female births, instead of the proportion of male to total births. If Z is the ratio, 7.e. Z=plq, show that the standard error of Z is approximately (1 +a2n/ Z n n being large, so that deviations are small compared with the mean. (The student may find it useful to refer to § 8, Chap. XI.) * Based on the mid-value of the class-interval for single rows, or the harmonic mean of the mid-values for groups of rows.

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