Download Statistics 1 by Keijo Ruohonen PDF

By Keijo Ruohonen

(Translation by way of Jukka-Pekka Humaloja and Robert Piché)

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The one-tailed hypothesis pairs are H0 : θ = θ0 vs. H1 : θ > θ0 H0 : θ = θ0 vs. H1 : θ < θ0 , and where the reference value θ0 is given. The pair H0 : θ = θ0 vs. H1 : θ > θ0 is tested at the level of significance α by calculating from the realized sample the lower 100(1 − α) % confidence limit θˆL for parameter θ in the manner presented earlier. The null hypothesis H0 is rejected if the reference value θ0 isn’t included in the obtained confidence interval, in other words if θ0 ≤ θˆL . Correspondingly, the pair H0 : θ = θ0 vs.

The hypothesis pair to be tested is thus H0 : σ12 = σ22 vs. H1 : σ12 = σ22 (and so k = 1). 10. 1789 (with 9 and 9 degrees of freedom) and the critical region consists of the values that aren’t included in that interval. 64, and it’s not in the critical region. No proof about the inequality of the variances was obtained, so H0 isn’t rejected. 14] Graphical Methods for Comparing Means A glimpse to a graphical display obtained from the population often gives quite a good image about the matter, at least when considering the expectations.

P(Tk ) = pk are supposed to be known, which is the null hypothesis H0 of the test. The alternative hypothesis H1 is that at least for one i P(Ti ) = pi . For the test, let’s take a sample with n elements, from which we determine the realized (absolute) frequencies f1 , . . , fk of the cases T1 , . . , Tk . These can be also considered to be random variables F1 , . . , Fk and E(Fi ) = npi . The test is based on the fact that the random variable k H= i=1 (Fi − npi )2 npi has nearly the χ2 -distribution with k − 1 degrees of freedom.

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