Which statements about the corresponding test statistics are correct? Whlen Sie eine oder mehrere Antworten: a. Taking the difference of the 2 means of the respective groups, we achieve the same result we would have gotten by the Kolmogorov-Smirnov statistic. b. For H_0: F_X(x) = F_Y(x), a small value of the Kolmogorov-Smirnov statistic yields enough evidence to reject the assumption that the two groups are distributed in the same way. c. For H_0: F_X(x) = F_Y(x), a large value of the Kolmogorov-Smirnov statistic yields enough evidence to reject the assumption that the two groups are distributed in the same way. Od. Having evaluated an arbitrary test statistic t(X), where X is our sample, we always reject when the test statistic is large. What is true about densities and distributions? Whlen Sie eine oder mehrere Antworten: a. The cumulative distribution at y is the density integrated up to y. b. The cumulative distribution is like a smooth histogram and indicates how likely a random variable takes a value in a specific region. c. The cumulative distribution function is strictly increasing everywhere for all distributions. Therefore it can never quite reach 0 or 1. Od. If the density of a population at a point x is smaller than the one of another population, then also the cumulative distribution function of the first population is smaller than the other one. Which statements about the permutation test is true? Whlen Sie eine oder mehrere Antworten: a. A permutation test can be used to approximate distributions of various test statistics on a given data set which is sampled from an unknown distribution. Ob. The number of permutations of 100 datapoints is larger than the number of atoms in the universe. c. A permutation test does not require to know the distribution of the test statistic for statistical testing. O d. The permutation test relies on resampling from a given dataset without replacement.