The original data were slightly modified to simplify the analysis; the data to be used for this project are provided in the file Waves. cav together with this task sheet. The file contains the following variables, with each row giving data for a half-hour time period: Month - the month integer 1, ...,12 Day - the year [integer 1, . ..,31] Hour - the start of the time period [half integer 0...,23.5] MaxHeight - the maximum wave height in metres [decimal] Direction - the predominant direction of the waves 8 cate- gories: N, NE, E, SE, S, SW, W, NW](c) Mean maximum wave height vs. wave direction We want to test whether there is evidence that the mean maximum wave height depends on the predominant direction of the waves. (i) [1 mark] Formulate an appropriate hypothesis test, and ex- plain which statistical method should be used to conduct the test. (ii) [0.5 marks] Compute the test statistic of the data. (iii) [0.5 marks] Compute the p-value of the data, and state the test decision at a significance level of 1%. (iv) [0.5 marks] Discuss whether or not it makes sense to conduct pairwise t-tests for the given data. (v) [1 mark] Explain how you could use randomisation to estimate the p-value of the data. Discuss in particular the number of randomisation samples that would have to be created to get an accurate estimate of the p-value for the given data