By Brumback B. A.

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This problem uses the exponential distribution to calculate an array of IQR’’s of the bootstrapped data. 3 Conﬁdence Intervals 23 distribution to the data set A #Then uses a parametric bootstrap to get a 90% confidence interval for the IQR of the population from which the data set A was taken. 95)) Resampling Stats ’The following program fits an exponential distribution to the data set A ’Then uses a parametric bootstrap to get a 90% confidence interval for the IQR of the ’population from which the data set A was taken.

As it is difﬁcult to test such a hypothesis, we normally would perform an initial transformation of the data, subtracting three from each of the observations in the vitamin-E-treated sample. 5 In the present example, when we rejected the null hypothesis, we accepted the alternative that vitamin E had a beneﬁcial effect. Such a test is termed one-sided. A two-sided test would also guard against the possibility that vitamin E had a detrimental effect. A two-sided test would reject for both extremely large and extremely small values of our test statistic.

We say that we make a Type II error when we accept the primary hypothesis, yet an alternative is true. Before we analyze data, we establish a set of values for the test statistic for which we will reject the primary hypothesis known as the rejection region. Its complement, the set of values for the test statistic for which we will accept the primary hypothesis is known as the acceptance region. The boundaries separating these regions are chosen so that the signiﬁcance level, deﬁned as the probability of making a Type I error, will be less than some ﬁxed value.