Question 1. [7 marks] [Chapter 3] A group of students was interested in comparing three different methods of juicing oranges. They purchased a selection of oranges from a supermarket. The oranges were randomly divided into three groups one group of oranges was juiced by hand, the second group was individually microwaved for 20 seconds and then juiced by hand, the third group was juiced using a mechanical citrus juicer. The data for this comparison is stored in the file Orange4.csv which can be downloaded from Canvas. The data contains 2 variables: More75 Whether or not the orange yielded more than 75mls of juice (Yes or No) Method The method used to juice the orange (Hand, Micro or Juicer). Watch the movie about using VITOnline for randomisation tests on Canvas Or Download the VIT Guide for Randomisation Tests from Canvas. Use these Guides and the relevant parts of Chapter 3 lecture recordings while working on this question. (a) Briefly explain why this study is an experiment. [1 Mark] (b) (i) Load the file Orange4.csv into VITOnline or iNZightVIT. Run a randomisation test to see if the proportion of oranges that yielded more than 75 mls of juice differed between the three juicing methods. Include the output from this in your assignment answers. [1 Mark] . Notes: Variable 1 needs to be More75 and Variable 2 needs to be Method. VITOnline: Before you select Analyse choose the category to focus on as Yes iNZightVIT: 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 of oranges that yielded more than 75 mls of juice at least as big as the observed average deviation 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 of oranges that yielded more than 75 mls of juice can be explained by chance acting alone? Briefly justify your answer. [1 Mark] (iv) Can we conclude that different juicing methods caused the differences in the proportions of oranges that yielded more than 75 mls of juice? If so, justify why with two reasons. If not, what can we conclude? [3 Marks]