The following table gives data from the 2011 UK Census, on a simple random sample of 10 parliamentary constituencies drawn from all the constituencies in England and Wales. The data for each constituency are x, the total number of full-time students living in the constituency (during term time, in thousands) and y, the total numbers of cars and vans available to all households in the constituency (in thousands). Constituency X y Bermondsey and Old Southwark 17.2 23.5 Bexhill and Battle 4.1 62.0 Birmingham, Perry Barr 10.2 36.5 Bolsover 3.9 50.3 Buckingham 5.0 66.0 Chorley 4.0 54.4 Hyndburn 4.8 42.1 Mitcham and Morden 8.5 34.5 Monmouth 3.8 51.3 Stratford-on-Avon 3.6 59.2 For these data Ex = 65.1, Ey = 479.8, >x2 = 595.59, Vy = 24672.94 and Exy = 2677.86. Calculate the correlation coefficient for these two variables, and type the answer, rounded to two decimal places, in the box below. Answer:An experiment was carried out to compare the wear resistance of two different materials for making the soles of children's shoes. Special pairs of shoes were made up with one shoe sole in Material A and the other in Material B. (Either the right or the left shoe was chosen at random to have the Material A sole.) Children were then given the shoes and asked to wear them normally for two months. At the end of that time, the amount of wear (in mm) of each sole was measured. at the centre of the sole. The differenoes in wear amounts (Material A - Material B) were calculated. In all there were 14 pairs of shoes. The sample mean of the differences was 0.212 mm, and the standard deviation of the differences was 0.131 mm. Using a method based on the matched-pairs t-test, calculate a 95% condence interval for the difference between the mean wear amounts for the two materials. Round the end points of your interval to three decimal plaoes and choose the appropriate option. Select one: 0 (0.173. 0.243) (0.071. 0.495) (0.177. 0.247) (0.133. 0.233) (0.137. 0.237) (0.134. 0.290) (0.045. 0.439) OOOOOOO (0.143. 0.231) Select the TWO options that are TRUE statements about clinical trials. Select one or more: CI D In a clinical trial with a matched-pairs design, paired individuals need not necessarily have the same gender. In order to avoid selection bias, in a placebo-controlled matched-pairs clinical trial the rst person in each pair must always be given the placebo. In a placebo-controlled clinical trial with a crossover design, all the patients receive the placebo rst and then change over to the drug under test. In a double-blind clinical trial, neither the patients nor the researchers assessing the outcomes of the treatments know which treatment each patient has received. However, there is an independent person (perhaps a pharmacist) who does know which treatment each patient has received. In a double-blind clinical trial, the researchers who assess the outcomes of the treatments do not actually see the patients, but instead make their assessment solely on the basis of the information in the patients' records (which, of course, include details of which treatments they are receiving). The patients are not allowed to see the records till the trial is over