Q3 Ten form 1 students from a secondary school measured how far they could push the shot-put with their dominant (writing) hand and their weaker (non-writing) hand. They thought that they could push equal distances with either hand. The data were collected and recorded in the following table. Distance (in feet) using student 1 student 2 student 3 student 4 student 5 student 6 student 7 student 8 student 9 student 10 Dominant hand 30 26 34 17 19 26 20 24 30 18 Weaker hand 28 15 27 18 17 26 16 18 25 16 (a) Conduct a hypothesis test to determine whether the mean difference in distances between the student's dominant versus weaker hands is significant using 5% significant level. (b) State the assumption needed for the test in (a). (c) Find the range of the p-value in (a). (d) The sports teacher of this secondary school selects another 12 form 1 students to push the shot-put and find the 95% confidence interval for the mean difference in distances between the student's dominant versus weaker hands to be (1.356, 5.666). Find the mean and standard deviation of these twelve form 1 students. (20 marks)