NOTE: Maintain Two Decimal Places for all Calculations. Qn.1: A survey was conducted on people aged 21 to 60 to investigate their level of difcult in sight. as recorded in the table given. with the data below. Age Group Responses for Difficult in Sight Very High High Low Very Low 21 25 2 0 3 1 26 30 5 6 2 3 31 35 8 2 2 l 36 40 10 8 4 5 41 45 5 9 1 5 46 50 10 5 l 3 51 55 15 2 2 l 56 60 20 5 8 9 a) Determine the total number of respondents per age group (4 NIarks) 1:) Calculate the respondents' average age (4 Marks) e) With your results of c) above compute; {i} The standard deviation (SD) for the respondents' age (7 .'MarksJ (ii) The standard error (SE) for the data (3 Marks) {iii} Determine the quartiles 1,2, and 3. as well their interquartile range (7 Nlarks) {iv} Plot out a frequency polygon for these score (5 hiarks) Total 30 Marks Qn.2: A tobacco company statistician wishes to know whether heavy smoking is related to longevity. From a sample of recently deceased smokers, the number of cigarettes (estimated per day for their last five years after visits with their surviving relatives) is paired with the number of years that they lived. Cigarettes (y) 25 35 10 40 85 75 60 45 50 Years Lived (x) 63 68 72 62 65 46 51 60 55 a) Plot out a scatter graph for these data (4 Marks) b) Determine the Spearman's rank correlation coefficient (6 Marks) c) Compute the coefficient of determination (2 Marks) d) Explain and give an interpretation of your results as above (2 Marks) e) Calculate the student's t-statistics (3 Marks) f) At 5% level of significancy, test the hypothesis that; there is no relationship between cigarette smoking and years lived (3 Marks) Total 20 Marks CU Qn.3: With the random values of x as {52, 11, 75, 30, 92, 23, 101, 84, 61} a) Determine the median value (3 Marks) NDISH b) Prove that Arithmetic Mean > Geometric Mean > Harmonic Mean (6 Marks) c) Calculate the mean deviation from median (3 Marks) d) Compute the data's variance value (5 Marks) e) Determine the data's coefficient of variation (3 Marks) Total 20 Marks