Computation of the Expected Value of the Interval Width in the Small-Sample Case

istatistiğin esas amacı, öraeklemin sahip olduğu bilgilerden yararlanarak, kitle hakkında netice çıkarmak, kitlenin parametrelerini tahmin etmektir. Dikkat etmemiz gereken bir nokta, kitle ortalaması D için, student's t dağılımına dayanan, küçük örneklem güven aralığı tesadüfi bir genişliğe sahiptir (halbuki geniş-örneklem güven aralığının genişliği tesadüfi değildir). Bu makalenin amacı küçük örneklem göz önüne alındığında, aralık genişliğinin ortalama değeri, diğer bir deyişle beklenen değerini hesaplayabilecek yöntemi ortaya koyabilmektir.

The objective of many statistical investigations is to make inferences about population parameters based on sample data. Often these inferences are in the form of estimates, either point estimates[2] on interval estimates. We must note that the small-sample confidence interval for D, based on student's t (see section IV),possesses a random width [in contrast to the large-sample confidence interval (see section III), where the width is nonrandom]. In this paper our aim is to find the expected value of interval width in the samll-sample case.

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