Question 1 (Unit 6] 13 marks (a) A researcher is interested in studying childhood obesity in the UK. She downloads some data from the government website relating to overweight children. This data was collected through the National Child Measurement Programme (NCMP) and a child is dened as obese based on their BMI measurement. The latest data. that she nds are for the period 2019 to 2020; these data are split by ethnicity and given for children aged 4 to 5 years old and 10 to 11 years old. The number of children in these age ranges that are not considered to be obese is also given . The data are summarised and shown in Table 1. Table 1 Ethnicity Obese Not obese Obese Not obese Total 45 yr olds 45 yr olds 1011 yr olds 1011 yr olds Asian 3537 33241 12463 36837 Black 14800 7468 17646 Mixed 2194 19171 5413 17766 thite 24240 227637 60565 251319 Chinese or Other 1062 9830 9522 23512 Unknown 5764 55387 14355 54636 '1th 39404 In this question we will consider the case where one child is selected at random from the above dataset. (i) Complete Table 1 by calculating the missing entries, and the column, row and overall totals. Present these as part of a table. [3] (ii) Calculate the probability that the selected child is obese and is 4 to 5 years old. [2] (iii) Calculate the probability that the selected child is Asian, not obese and is 4 to 5 years old. [2] (iv) Calculate the probability that a 10 to 11 year old obese child is not white. Show all of your working. [3] page 3 of 11 (b) Femi, Fatina and Fintan enjoy going to concerts at their local open air music venue. The probability that Femi is going to a concert is 0.15, for Fatina this probability is 0.2, and for Fintan this probability is 0.25. For an upcoming concert, what is the probability that all three will go? State any important assumption that you make in order to calculate this probability. [3] Question 2 (Unit 6) - 12 marks A scientist wants to investigate the effects of climate change in the UK. The amount of rainfall in 12 regions of the United Kingdom, as estimated by the Met Office using data from weather stations in each region, is recorded below for February 2008 and 2018. Table 2 gives the total rainfall, in mm, along with the differences between the rainfall in February 2008 and 2018. 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 10.9 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. [2] (b) Record the number of values lying above and the number lying below the hypothesised value. What is the value of the test statistic? [2] (c) What is the appropriate critical value at the 5% significance level? [1] (d) Decide whether or not you would reject the hypothesis at the 5% significance level. [1] (e) Using Figure 6 of Unit 6 (Subsection 4.1), calculate the p-value given by the hypothesis test. [3] (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? [1] (g) How does this conclusion sit with the result of part (d)? [1] (h) What is your overall conclusion in terms of the difference in rainfall in February 2008 and February 2018, based on these data? [1]\f-- I Interpretation of pvalues pvalue Rough interpretation p > 0.10 Little evidence against the hypothesis 0.10 2 p > 0.05 Weak evidence against the hypothesis 0.05 2 p > 0.01 Moderate evidence against the hypothesis 0.01 2 p > 0.001 Strong evidence against the hypothesis 0.001 2 p Very strong evidence against the hypothesis