Table 2 Region Rainfall (mm) Rainfall (mm) Difference (mm) Feb 2008 Feb 2018 2018-2008 England N and NE 33.3 46.7 13.4 England North 51.1 54.7 3.6 England South 30.4 39.5 9.1 Midlands 36.7 34.6 -2.1 England NW and N Wales 80.8 76.2 -4.6 England SW and S Wales 60.4 62.6 2.2 East Anglia 18.7 40.3 21.6 England SE and Central 26.5 40.9 14.4 Scotland West 176.8 116.7 -60.1 Scotland East 87.1 57.3 -29.8 Scotland North 206.7 98.4 -108.3 Northern Ireland 60.7 74.0 13.3 A sign test is to be performed to investigate whether the rainfall in February 2018 differs from the rainfall in February 2008. (a) Write down the hypothesis to be tested. (b) Record the number of values lying above and the number lying below the hypothesised value. What is the value of the test statistic? (c) What is the appropriate critical value at the 5% significance level? (d) Decide whether or not you would reject the hypothesis at the 5% significance level (e) Using Figure 6 of Unit 6 (Subsection 4.1), calculate the p-value given by the hypothesis test. (f) Looking at this p-value, and using Table 10 of Unit 6 (Subsection 5.1), what conclusion can be drawn from the hypothesis test? ) How does this conclusion sit with the result of part (d)? (h) What is your overall conclusion in terms of the difference in rainfall in February 2008 and February 2018, based on these data