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Bounded length sequential intervals
Lapšanská, Alica ; Hušková, Marie (advisor) ; Hlávka, Zdeněk (referee)
The Bachelor's thesis concerns the construction of bounded length sequential intervals with predetermined confidence. This paper analyses some methods, which solve this problem. In the first part we deal with a special case of random sample from normal population. For a known variance we use knowledge from nonsequential theory of interval estimation. We describe Stein's two-stage procedure for an unknown variance. Furthermore, we determine expected value of total sample range for various interval lengths. The second part generally considers a random sample from population with unknown finite variance. We present modified Stein's procedure and sequential Wald's procedure. Finally using simulation, we endeavor to find out a distribution of random variable, which corresponds to the sample range in case of unknown variance. We do this for all of the three mentioned procedures.
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Bounded length sequential intervals
Lapšanská, Alica ; Hušková, Marie (advisor) ; Hlávka, Zdeněk (referee)
The Bachelor's thesis concerns the construction of bounded length sequential intervals with predetermined confidence. This paper analyses some methods, which solve this problem. In the first part we deal with a special case of random sample from normal population. For a known variance we use knowledge from nonsequential theory of interval estimation. We describe Stein's two-stage procedure for an unknown variance. Furthermore, we determine expected value of total sample range for various interval lengths. The second part generally considers a random sample from population with unknown finite variance. We present modified Stein's procedure and sequential Wald's procedure. Finally using simulation, we endeavor to find out a distribution of random variable, which corresponds to the sample range in case of unknown variance. We do this for all of the three mentioned procedures.
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Statistical tests power analysis
Kubrycht, Pavel ; Malá, Ivana (advisor) ; Bílková, Diana (referee)
This Thesis deals with the power of a statistical test and the associated problem of determining the appropriate sample size. It should be large enough to meet the requirements of the probabilities of errors of both the first and second kind. The aim of this Thesis is to demonstrate theoretical methods that result in derivation of formulas for minimum sample size determination. For this Thesis, three important probability distributions have been chosen: Normal, Bernoulli, and Exponential.
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