Problem 1 Does your spinal column spinal change when you go about your daily business? Researchers investigated this problem. They collected data for an SR8 of adults and measured their heights upon awakening and upon going to sleep. The difference in heights in millimetres for each person was computed by difference = teakeuphetgrht sleephes'ght and is as follows: 3,0, 1D,13,-1,1,2,1,-2,8,3,1,IJ Conduct a hypothesis test, to investigate ifthe mean length of height changes during the day. Use a: = l].l]5. Hint: Show work for all steps DU, 0, 1, 2, 3, 4, 5, 6 and 1". Problem 2 a} How does the sample size required change in order to detect small, medium and large effect sizes? o} Produce a graph that shows this change. c] Why does the sample size required change with effect size? Hints: Cohen {1988} suggests that values of {1.2, I15 and [1.8 represent small, medium and large effect sizes, represectlyely. Determine the sample size required for an 30% chance of correctly rejecting the null hypothesis with a 10% chance of incorrectly rejecting the null hypothesis. Use a two-sided, one sample ttest procedure