Question 1. [7 marks] [Chapter 3] In a recent test of the effectiveness of a new sleeping pill, '35 volunteers were randomly assigned to three groups of 25. The rst group was given the new drug, the second group was given a placebo and the third group was given no treatment at all. Whether or not the volunteer managed to fall asleep in under 30 minutes was recorded. The data for this study is stored in the le \"5 leep . csv\" which can be downloaded from Canvas. The data contains 2 variables: Treatment The treatment group the volunteer was assigned to (either Drug, Placebo or Neither). Sleep Whether the volunteer fell asleep within 3D minutes (either Yes or No). Download the VIT Guide for Randomisatiou Tests from Canvas. Use the Guide while working on this question. (a) Briey explain why this study is an experiment. [1 Mark] (b) (i) Run the VIT software and load the le Sleep . csv into it. Run a randomisation test to compare the proportion of volunteers who fell asleep within 30 minutes between the three treatment groups. Include the output 'om this in your assignment answers. [1 Mark] Notes: Variable 1 needs to be Sleep and Variable 2 needs to be Treatment. Before you select \"Record my Choice\" in the Analyse window, change the level of interest to \"Yes\". (ii) When chance is acting alone, estimate how unusual it is to get an average deviation from the overall proportion who fell asleep at least as big as the observed difference in the experiment. (Use your randomisation test output to answer this.) [1 Mark] (iii) Is it plausible that the observed average deviation from the overall proportion who fell asleep can be explained by \"chance acting alone\"? Briey justify your answer. [1 Mark] (iv) Can we conclude that di'erent treatments caused di'erences in the sleep rate? If so, justify why with two reasons. If not, what can the manager conclude? [3 Marks]