Use a Kolmogorov Smirnov (KS) Test in order to determine if the following data set comes from an Exponential distribution with mean equal to five Data 0.433577647 1.077296386 1.461024528 2.037106422 3.671167985 3.724253017 3.815970293 3.905489821 6.842680422 6.933953839 Can we reject the hypothesis that the data come from an exponential distribution with a mean equal to five? Select one: O True O FalseComparing the Kolmogorov-Lilliefors and Kolmogorov-Smirnov Tests 1 point possible (graded) Let X1, ..., Xn ~ P with continuous cdf F. Consider the following two hypothesis tests. Hypothesis Test 1:(Kolmogorov-Smirnov) For the Kolmogorov-Smirnov test, our goal is to decide between a null and alternative hypothesis of the form Ho : F = 10,1 H1 : F # 40,1 The Kolmogorov-Smirnov uses the test statistic In = Vn sup | Fn (1) - Do, 1 and the test Wn = 1(Tn > qn) where qn denotes the 1 - 7 quantile of In. You choose , such that qn = 0.5. Hypothesis Test 2:(Kolmogorov-Lilliefors) For the Kolmogorov-Lilliefors test, our goal is to decide between a null and alternative hypothesis of the form HO: P E ( N ( 1, 0 ) ) MER, 0320 A1 : P = (N ( H, O') ) HER, 0320 The Kolmogorov-Lilliefors test uses the test statistic In = Vn sup | Fn (1) - DM,64 and the test Wn = 1(T n > qu) where qv denotes the 1 - v quantile of T n. You choose v such that of = 0.5. Assume that the null hypotheses Ho and Ho hold for both hypothesis tests above. Which test has a greater probability of rejecting the null hypothesis? O Kolmogorov-Smirnov test O Kolmogorov-Lilliefors testQ.7 Do Q9.39 from Moore text, p.249. (6" ed: 09.36. p. 243). This randomized experiment involves more than I factor. It is an example of a 2-factorial randomised experiment. Explanatory variables and their levels 1. Response variable = (Be very specific!) 2. Total sample size required = Outline: NOTE: The main advantages of factorial experiments are... 1. 2.Find a short textfarticle that contains an example of poor statistical reasoning and provide an analysis {in your own words} of why it illustrates bad statistical reasoning Your analysis should consist of 250-500 words and discuss one or more of'the fallacies or common errors that we have discussed in weeks 9-11 For example, it could illustrate Simpson's paradox, the Prosecutor's fallacy, inappropriate assumption of independence, generalising inappropriatelyfrom a biased sample, assuming correlation implies causation, regression to the mean it is okayto reuse an article from the weekly discussion fomms However, your analysis should be your own original work and in your own words Example: Analysis of textfartlcle: Peer Assisted Study Sessions {PASS} Statistical reasoning typels} relevant to this artide include "Selfselected samples', 'Confountng variables', "Cause and effect", 'Randomised experiment", "Averages". 11te implicit argument being made here is that students should attend PASS sessions as it will help them eam higher grades and reduce the risk of withdrawing from a unit. A potential problem with this line of reasoning is thatthe students who chooseto attend PASS sessions are self-selecting and that they might be ltelyto possess attributes that naturally make them more likelyto do well in units. For example, possible confounding variables that might be associated both with attending PASS and earning high grades are having sufficient spare time to devote to study, and intrinsic levels of motivation. As a general principle it is hard to determine cause and e'ecron the basis of an association unless data come from a randomised expenmewtor if possible confounding variables can be identied and controlled for. One way to try and control for confounding variables in this situation would be to compare the average gradesof students who attend PASS sessions to the average grades of students who do not attend PASS sessions but for units in which PASS is not available. If the tfference in average grades remained it would stggestthatthe observed differences may be due to confountng variables, whereas ifthe tfference disappeared or was less prominentthat would suggest that PASS does indeed help improve grades it does not seem like it would be practically possible to do a randomised controlled trial in this situation