A group of students was interested in comparing three different methods of juicing oranges. They purchased...

  

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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. (b) (i) Load the file Orange 4.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. Notes: Variable 1 needs to be More 75 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.) (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. Randomisation Test module: Randomisation Test; file: Orange4.csv; variable: More75,c Method,c; More75 Method Hand Yes No No No Yes No No No No No No Yes Yes No Yes No No No No No No Yes No Yes Yes No Yes No Yes No Yes Yes Yes Voc Hand Hand Hand Hand Hand Hand Hand Hand Hand Hand Hand Hand Hand Hand Hand Hand Hand Hand Hand Juicer Juicer Juicer Juicer Juicer Juicer Juicer Juicer Juicer Juicer Juicer Juicer Juicer Juicer Re-randomised Hand Micro Juicer Hand Micro Juicer Micro Micro Hand Hand Juicer Juicer Juicer Juicer Micro Juicer Hand Micro Juicer Micro Micro Hand Micro Micro Micro Micro Hand Hand Juicer Juicer Juicer Juicer Juicer Uand Data Yes Yes Yes 0.0 00500 0.1 0.2 Re-Randomised Data Yes Yes Yes 0.0 0.0 OO 6 0.1 8 0.2 0.1 0.3 Re-Randomisation Distribution No 23/1000 = 0.023 O 0.2 0.17 X 14 XXXXX 0.3 XXXX 13 No No 0.3 0.4 No 0.4 0.4 0.5 0.5 0.5 15 0.6 0.6 0.6 12 No No 14 0.7 12 0.7 0.7 0.8 0.8 0.8 7 0.9 0.9 0.9 Hand Micro Juicer 1.0 Hand Micro Juicer 1.0 1.0 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. (b) (i) Load the file Orange 4.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. Notes: Variable 1 needs to be More 75 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.) (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. Randomisation Test module: Randomisation Test; file: Orange4.csv; variable: More75,c Method,c; More75 Method Hand Yes No No No Yes No No No No No No Yes Yes No Yes No No No No No No Yes No Yes Yes No Yes No Yes No Yes Yes Yes Voc Hand Hand Hand Hand Hand Hand Hand Hand Hand Hand Hand Hand Hand Hand Hand Hand Hand Hand Hand Juicer Juicer Juicer Juicer Juicer Juicer Juicer Juicer Juicer Juicer Juicer Juicer Juicer Juicer Re-randomised Hand Micro Juicer Hand Micro Juicer Micro Micro Hand Hand Juicer Juicer Juicer Juicer Micro Juicer Hand Micro Juicer Micro Micro Hand Micro Micro Micro Micro Hand Hand Juicer Juicer Juicer Juicer Juicer Uand Data Yes Yes Yes 0.0 00500 0.1 0.2 Re-Randomised Data Yes Yes Yes 0.0 0.0 OO 6 0.1 8 0.2 0.1 0.3 Re-Randomisation Distribution No 23/1000 = 0.023 O 0.2 0.17 X 14 XXXXX 0.3 XXXX 13 No No 0.3 0.4 No 0.4 0.4 0.5 0.5 0.5 15 0.6 0.6 0.6 12 No No 14 0.7 12 0.7 0.7 0.8 0.8 0.8 7 0.9 0.9 0.9 Hand Micro Juicer 1.0 Hand Micro Juicer 1.0 1.0